A cubic polynomial with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1

(a) Let X and Y be the arrival times of buses A and B respectively, it is given that buses A and B are independent and hence X and Y are independent random variables.

Therefore, X and Y are also degenerate at c.

Since a person arrives at the bus stop at time 0, the arrival times of buses A and B cannot be negative

i.e., X, Y ≥ 0.

Also, both buses cannot arrive at time 0

i.e., P(X = 0, Y = 0) = 0.

Now, suppose that X and Y are not degenerate. T

hen, their joint distribution function is given by:

F(X, Y) = P(X ≤ x, Y ≤ y) > 0, for some x, y ≥ 0.

Using the independence of X and Y, we get:

F(X, Y) = P(X ≤ x)P(Y ≤ y) > 0,

for some x, y ≥ 0.

Since P(XY = 0) = 0,

we have XY ≠ 0 and

hence P(XY = c) > 0,

for some c ≠ 0.

Now, for a fixed ε > 0,

let Bε = {(x, y) : |xy - c| < ε}.

Then, P((X, Y) ∈ Bε) > 0.

Similarly, let B'ε = {(x, y) : x < ε} and

B''ε = {(x, y) : y < ε}.

Then, P((X, Y) ∈ B'ε) > 0

and P((X, Y) ∈ B''ε) > 0.

Now, we have:

Bε ⊆ B'ε ∪ B''ε and (X, Y) ∈ B'ε

if and only if X < ε and (X, Y) ∈ B''ε

if and only if Y < ε.So,

using the union bound and taking ε small enough, we get:

P(X < ε) + P(Y < ε) > P((X, Y) ∈ Bε) > 0.

This contradicts the assumption that P(X = 0, Y = 0) = 0.

Therefore, X and Y must be degenerate.

Now, we will show that if XY is degenerate at c ≠ 0

i.e., P(XY = c) = 1,

then X and Y are also degenerate at the same point.

To see this, note that for any Borel sets A, B ⊆ R, we have:

P(X ∈ A, Y ∈ B) = P(XY ∈ A × B) = P(XY = c)

= 1, if (c ∈ A × B) or (c is an isolated point of A × B).

Therefore, X and Y are also degenerate at c.

This completes the proof of the required statement.

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While playing, they move, but still maintain the sinusoidal function, ... 5.At the end of the performance, the band marches off the field to the ... Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line.

Answer:

#1

#2

#3

#4

Answer:

https://brainly.com/question/3677306

Step-by-step explanation:

Answer:

1. 0=0

2. x= -3

3. 14=0

Step-by-step explanation:

I tried I'm sorry if it's wrong

The given integral is: $$\int (-2x^2 + 500)dx$$

To solve the above integral, we integrate both terms separately. Using the integral formulas, $$\int x^n dx= \frac{x^{n+1}}{n+1}+ C$$$$\int kf(x)dx= k\int f(x)dx$$

where C is a constant of integration and k is a constant.

The integral $\int -2x^2 dx$ is:\begin{align*} \int -2x^2 dx &= -2\int x^2 dx\\&= -2\times \frac{x^{2+1}} {2+1} + C\\&= -\frac {2}{3}x^3+ C\end{align*}

The integral $\int 500 dx$ is:\begin{align*}\int 500 dx &= 500\int dx\\&= 500\times x + C\\&= 500x + C\end{align*}

Thus, the integral $\int (-2x^2 + 500) dx$ is:\begin{align*}\int (-2x^2 + 500) dx &= \int -2x^2 dx + \int 500 dx\\&= (-\frac {2}{3}x^3+ C_1) + (500x + C_2)\\&= -\frac {2}{3}x^3+ 500x + C\end{align*}

where C is a constant of integration and $C=C_1+C_2$.

Therefore, the exact value of the integral is $-\frac {2}{3}x^3+ 500x + C$.

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Answer:

2 and 5

Step-by-step explanation:

2×5 = 10 or visa versa

10 ÷5=2

10 ÷2 =5

Answer:

y=9

Step-by-step explanation:

12/y=4/3

3×12/y=3×4/3

36/y=4

y×36/y= 4×y

36=4y

36/4=4y/4

9=y

Answer:

Step-by-step explanation:

1.  Not sure...

2. $ 1.44

3. $ 3.70

4. $11 per ticket

Answer:

I was unable to see this link. Sorry.

Step-by-step explanation:

Answer:

quadratic equation

Step-by-step explanation:

Answer:

the equation shown here is a quadratic equation

The sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:

2, 3, 2, -12, -88, -432, ...

To define the sequence {aₙ}, given a₀ = 2, a₁ = 3, and the recursive formula aₙ = 6aₙ₋₁ - 8aₙ₋₂, we can calculate the subsequent terms of the sequence.

Using the given initial conditions, we have:

a₀ = 2

a₁ = 3

To find a₂, we substitute n = 2 into the recursive formula:

a₂ = 6a₁ - 8a₀

   = 6(3) - 8(2)

   = 18 - 16

   = 2

To find a₃, we substitute n = 3 into the recursive formula:

a₃ = 6a₂ - 8a₁

   = 6(2) - 8(3)

   = 12 - 24

   = -12

Continuing this process, we can find the subsequent terms of the sequence:

a₄ = 6a₃ - 8a₂

   = 6(-12) - 8(2)

   = -72 - 16

   = -88

a₅ = 6a₄ - 8a₃

   = 6(-88) - 8(-12)

   = -528 + 96

   = -432

and so on.

Therefore, the sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:

2, 3, 2, -12, -88, -432, ...

Please note that if you need the general formula for the nth term of the sequence, it may require a different approach as the given recursive formula is not a linear recurrence relation with constant coefficients.

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When performing polynomial regression, it is advisable to use the smallest degree that provides a good fit.

Polynomial regression involves fitting a polynomial function to a set of data points. The degree of the polynomial represents the highest power of the independent variable in the equation.

By using the smallest degree that provides a good fit, we aim to strike a balance between model complexity and overfitting.

Using a smaller degree helps prevent overfitting, which occurs when a model becomes too complex and captures noise or random fluctuations in the data. Overfitting leads to poor generalization, meaning the model may perform well on the training data but poorly on new, unseen data.

By using the smallest degree that provides a good fit, we minimize the risk of overfitting and ensure that the model captures the underlying trend in the data without incorporating unnecessary complexity.

This approach helps create a more robust and reliable model for making predictions on new data.

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9514 1404 393

Answer:

  (d)  (-3, 1)

Step-by-step explanation:

We assume a typo in the problem statement, and that the equations are supposed to be ...

  [tex]2x -3y = -9\\-x +3y = 6[/tex]

Adding the two equations gives ...

  x = -3

Substituting for x in the second equation gives ...

  3 +3y = 6

  1 + y = 2 . . . . divide by 3

  y = 1 . . . . . . . subtract 1

The solution is (x, y) = (-3, 1).

Answer:

Where is the number I need to round to?

(Please don't give me a bad rating i'm trying to help :) )

Answer:

i dont know do it yourself chump

Step-by-step explanation:

Answer:

It would be D

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

To find the area of a triangle, multipy the base and height of a triangle, then divide it in half

8x9=72/2=36

Answer:

2:40

Step-by-step explanation:

Add 85 minutes to 45 minutes and then add that to 12:30

Answer:

The 16ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 9

Common Difference = (d) = 2

Now, For 16ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₁₆ = 7 + (16 - 1) × 2

a₁₆ = 7 + 15 × 5

a₁₆ = 7 + 75

a₁₆ = 82

Thus, The 16ᵗʰ term of this sequence is 82

-TheUnknownScientist

If a normal distribution with a mean of 7.5 and a standard deviation of 1.2. (a) The probability that a cookie has less than 9 chips is 0.8944. (b) The probability that a random sample of 4 cookies has an average of fewer than 9 chips per cookie is 0.9938.

As μ = 7.5, σ = 1.2. The number of chips in a given cookie is in a normal distribution. We need to estimate the following probabilities:

(a) For this, we need to identify the probability of a Z-score when X=9. We can calculate it using the formula,

Z = (X-μ)/σ.

Therefore,

Z = (9-7.5)/1.2 = 1.25.

Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 1.25. Using the calculator, P(Z &lt; 1.25) = 0.8944.

(b) For this, we need to identify the probability of the Z-score when X = 9, n=4. We can calculate it using the formula,

Z = (X-μ)/(σ/√n).

Therefore,

Z = (9-7.5)/(1.2/√4) = 2.5.

Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 2.5. Using the calculator, P(Z &lt; 2.5) = 0.9938.

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Answer:

Mean and IQR

Step-by-step explanation:

The measure of centre gives the central or the measure which gives the best mid term of a distribution. Based in the details of the box plot, the median is the value which divides the box in the box plot.

For company A:

Range = 25 to 80 with a median value at 30 ; this means the median does not give a good centre measure of the distribution ad it is very close to the minimum value. This goes for the Company B plot too; with values ranging from (35 to 90) and the median designated at 40.

Hence, the mean will be the best measure of centre rather Than the median in this case.

For the variability, the interquartile range would best suit the distribution. With the lower quartile and upper quartile both having reasonable width to the minimum and maximum value of the distribution.

Answer:

B

Step-by-step explanation:

Answer:

The circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Step-by-step explanation:

2r=d

2(8)=d

16=d

C=πd

C=π16

So, the circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Answer:

50.2654

Step-by-step explanation:

Answer:

1350 m³

Step-by-step explanation:

To find the volume of a rectangular prism, we have to multiply its length, width, and height together.

The dimensions of this prism are 9, 10, and 15.

9 · 10 · 15 = 1350

The volume is 1350 meters³.

I hope this helps ^^