Aiden works at a lab with a huge circular particle accelerator. It has a diameter of 8 kilometers. What is the accelerator's radius?

(1) To find the value of B that makes f_(XY)(x,y) a valid joint density function, we need to ensure that the total probability over the entire domain is equal to 1. In this case, the domain is |x|<1 and |y|<1.

The integral of f_(XY)(x,y) over the given domain should be equal to 1:

∫∫ f_(XY)(x,y) dx dy = 1

∫∫ B(1+xy) dx dy = 1

To solve this integral, we integrate with respect to x first and then with respect to y:

∫(∫ B(1+xy) dx) dy

∫[Bx + B(xy^2)/2] dy, integrating with respect to x

Bxy + B(xy^2)/2 + C, integrating with respect to y

Now, evaluate the integral over the given domain:

∫[-1,1] [Bxy + B(xy^2)/2 + C] dy

[Bxy^2/2 + B(xy^3)/6 + Cy] evaluated from -1 to 1

[B/2 + B/6 + C] - [-B/2 - B/6 - C]

(B/2 + B/6 + C) - (-B/2 - B/6 - C)

2B/3 = 1

Solving for B:

B = 3/2

Therefore, the value of B that makes f_(XY)(x,y) a valid joint density function is B = 3/2.

(2) To determine if X and Y are uncorrelated, we need to calculate the covariance between X and Y. If the covariance is zero, then X and Y are uncorrelated.

Cov(X, Y) = E[XY] - E[X]E[Y]

To calculate E[XY], we need to find the joint expectation:

E[XY] = ∫∫ xy f_(XY)(x,y) dx dy

E[XY] = ∫∫ xy (3/2)(1+xy) dx dy

Integrating over the domain |x|<1 and |y|<1, we can calculate E[XY].

Similarly, we need to calculate E[X] and E[Y] to determine Cov(X, Y).

If Cov(X, Y) is found to be zero, then X and Y are uncorrelated.

(3) To prove or disprove independence between X and Y, we need to check if the joint probability density function (pdf) can be factorized into the product of the marginal pdfs of X and Y.

If f_(XY)(x,y) = f_X(x)f_Y(y), then X and Y are independent.

To determine if this factorization holds, we need to compare the joint pdf f_(XY)(x,y) with the product of the marginal pdfs f_X(x) and f_Y(y). If they are equal, then X and Y are independent. Otherwise, they are dependent.

(4) To prove or disprove the independence between X^2 and Y^2, we follow a similar approach as in (3). We compare the joint pdf of X^2 and Y^2 with the product of their marginal pdfs. If they are equal, X^2 and Y^2 are independent. Otherwise, they are dependent.

By examining the factorization of the joint pdfs and comparing them with the product of the marginal pdfs, we can determine the independence relationships between the variables X, Y, X^2, and Y^2.

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Answer:

6 ft

Step-by-step explanation:

The triangle CDE is half of the size of triangle ABC, so if you match up the corresponding sides, DE is half of AC. AC is 12 so DE is 6.

hope is helped!

Answer:

28-8-4x=0

x=5

5 days

Step-by-step explanation:

28-8=20 problems left

then 4 each day

Answer:

It would decrease, but not necessarily by 8%

If the teacher had used a 90% confidence interval rather than a 98% confidence interval, the width of the interval would decrease, but not necessarily by 8%.

Option D is the correct answer.

A confidence interval is a range of values that is likely to contain the true value of an unknown parameter, such as a population means or proportion, based on a sample of data from that population.

It is a statistical measure of the degree of uncertainty or precision associated with a statistical estimate.

We have,

The width of a confidence interval is determined by the level of confidence and the sample size.

A higher confidence level requires a wider interval, and a larger sample size typically results in a narrower interval.

Since the sample size is fixed in this case, changing the confidence level will result in a change in the width of the interval.

As the confidence level increases, the width of the interval also increases. This is because a higher confidence level requires a larger margin of error, which is added to the point estimate to create the interval.

Therefore,

If the teacher had used a 90% confidence interval rather than a 98% confidence interval, the width of the interval would decrease, but not necessarily by 8%.

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The inverse Laplace transform of 1 / (3s² + 5s + 1) is f(t) = 1/2 × [tex]e^{(-t)[/tex]- 1/2 × [tex]e^{(-t/3)[/tex].

To find the inverse Laplace transform of the function F(s) = 1 / (3s² + 5s + 1), we can use partial fraction decomposition and reference tables for Laplace transforms.

Step 1: Factorize the denominator

Factorize the denominator of the function 3s² + 5s + 1 to find its roots:

3s² + 5s + 1 = (s + 1)(3s + 1)

Step 2: Write the partial fraction decomposition

Write the function F(s) as a sum of partial fractions:

F(s) = A / (s + 1) + B / (3s + 1)

Step 3: Determine the values of A and B

To find the values of A and B, we can multiply both sides of the equation by the common denominator and equate the numerators:

1 = A(3s + 1) + B(s + 1)

Expand the right side and collect like terms:

1 = (3A + B)s + (A + B)

By equating the coefficients of s and the constant terms on both sides, we get a system of equations:

3A + B = 0

A + B = 1

Solving this system of equations, we find A = 1/2 and B = -1/2.

Step 4: Write the inverse Laplace transform

Using the partial fraction decomposition, we can now write the inverse Laplace transform:

F(s) = 1/2 × (1 / (s + 1)) - 1/2 × (1 / (3s + 1))

Referring to Laplace transform tables, we find that the inverse Laplace transform of 1 / (s + a) is [tex]e^{(at)[/tex], and the inverse Laplace transform of 1 / (s - a) is [tex]e^{(at)[/tex]. Therefore, applying these results, we have:

f(t) = 1/2 × [tex]e^{(-t)[/tex] - 1/2 × [tex]e^{(-t/3)[/tex]

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Answer:

-18

Step-by-step explanation:

5a2-7-b3

[tex]5*a*2-7-b*3[/tex]

[tex]5\cdot \left(-2\right)\cdot \left(2\right)-7-\left(-3\right)\cdot 3[/tex]

Therefore, -18 is your answer.

Hope this helped! :)

The given recurrence relation is an = 400 - 5an-2 + 200-3, with initial values a0 = 1 and a1 = 2. We need to find an explicit formula for a(n).

To find an explicit formula for a(n), we will first solve the recurrence relation and then generalize the pattern. Let's expand the relation for a few terms to observe the pattern:

a2 = 400 - 5a0 + 200-3 = 400 - 5(1) + 200-3 = 397

a3 = 400 - 5a1 + 200-3 = 400 - 5(2) + 200-3 = 388

a4 = 400 - 5a2 + 200-3 = 400 - 5(397) + 200-3 = -9603

a5 = 400 - 5a3 + 200-3 = 400 - 5(388) + 200-3 = -1260

From the given examples, we can observe that the recurrence relation alternates between positive and negative values. This suggests that the relation might have a periodic pattern. Since the given recurrence is a second-order relation (in terms of n), it is reasonable to assume that the pattern repeats every two terms.

Based on this observation, we can establish the following explicit formula for a(n):

a(n) = (-1)^(n mod 2) * (200n - 5^(n/2) + 200-3)

In this formula, the term (-1)^(n mod 2) alternates between -1 and 1 depending on the parity of n, ensuring the alternating pattern. The other terms account for the linear and exponential components of the recurrence relation.

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Answer:

2) 4/5

3) 3

Step-by-step explanation:

2) 4/8-3=4/5

3)5x-4=3x+2

2x=6

x=3

Answer:

2) 4/5

3)x=3

Step-by-step explanation:

1) 4/8-3= 4/5

2) 5x-4=3x+2

bring 3x to left side and bring -4 to right side (remember signs will be reversed that is 3x becomes -3x and -4 will be 4

5x-3x=4+2

2x=6

x=6/2

x=3

put 3 in place of x

5*3-4=3*3+2

15-4=9+2

11=11

Answer: 6

Step-by-step explanation:

The total amount needed by Kallen for the gift and the wrapping paper will be:

= $43.87 + $2.94

= $46.81

Since he earns $8.25 for each lawn he mows, the number of lawns they he will need to complete to buy the gift and wrapping will be:

= $46.81 / $8.25

= 5.67

= 6 lawns approximately

He'll need to mow 6 lawns

Answer:

(5,6)

Step-by-step explanation:

I'm guessing you mean the coordinates for the point where the lines intersect

Answer:

I believe it is b: (5,6)

Explanation:

The point (5,6) is the only point on the graph that both lines go through.

Answer:

The answer is 440

Step-by-step explanation:

I just took the test and got that question right

Answer:

We meet again

Step-by-step explanation:

When a rectangle is dilated by a scale factor k, the length and width of the rectangle are both multiplied by k. In this case, the length of the rectangle is being dilated by a scale factor of 5. So the length of the rectangle after the dilation will be 20 * 5 = **100 meters**.

The last entry in the synthetic division table is not zero, 3i is not a zero of the polynomial function g(x) = x³ - 4x² + 9x - 36.

To determine if 3i is a zero of the polynomial function g(x) = x³ - 4x² + 9x - 36, we can use synthetic division.

First, we set up the synthetic division table:

   3i | 1   -4   9   -36

Performing the synthetic division:

      | (1)  (-4)   (9)   (-36)

   3i |        3i    9i²   27i

      | (1)  (-4 + 3i)   (9 + 9i²)   (-36 + 27i)

Simplifying the last row, we have:

      | (1)  (-4 + 3i)   (9 - 9)   (-36 + 27i)

      | (1)  (-4 + 3i)   (0)   (-36 + 27i)

Therefore, the last entry in the synthetic division table is not zero, 3i is not a zero of the polynomial function g(x) = x³ - 4x² + 9x - 36.

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Answer:

the slope is 3

the y intercept is (0,-7)

Step-by-step explanation:

3x-y=7 solve for y

add y to both sides

3x=7+y

subtract 7 from both sides

y=3x-7

y=mx+b

m=slope

b=y-intercept

3=slope

-7=y-intercept

Hope that helps :)

The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 130 minutes from a sample of 50 laptops, is approximately 0.0006 (rounded to four decimal places).

To calculate the p-value, we use the t-test. Given the null hypothesis that the average runtime is 120 minutes, the alternative hypothesis is that it is not equal to 120 minutes. We compare the sample mean to the hypothesized population mean using the t-distribution.

Using the formula for the t-statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (130 - 120) / (25 / sqrt(50))

t = 10 / (25 / 7.0711)

t = 2.8284

The degrees of freedom for the t-distribution are (sample size - 1) = (50 - 1) = 49.

Using the t-distribution table or statistical software, we find that the two-tailed p-value for a t-value of 2.8284 with 49 degrees of freedom is approximately 0.0006.

Therefore, the p-value for this hypothesis test is approximately 0.0006.

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Answer:

it's arm will regenerate and grow back

plz mark me as brainliest

Answer:

B. The arm will regenterate

Answer:

2

Step-by-step explanation:

60 divided by 28.3 which gives u 2.120141342756184

so round it which gives u 2

Answer:

1

EXPLAINATION:

y = mx +b

b = y intercept

Answer: f

=  x = − 3 x + 1 = x = 1 4 g = x 2 + 2 x − 5f( x ) = f ( x )

Step-by-step explanation:

Answer: should be 7819.20

explanation:

7200 * .043 * 2 = 619.20

7200 + 619.20 = 7819.20

To approximate the value of f(1.5) using the tangent line to the graph of f at x = 1, we first find the derivative of f(x) to determine the slope of the tangent line at x = 1. The derivative is f'(x) = -2 sin x. Evaluating f'(x) at x = 1, we find the slope to be approximately -1.6829.

Next, we use the point-slope form of a line to find the equation of the tangent line. We have the point (1, f(1)) ≈ (1, 1.5839) and the slope -1.6829. Plugging these values into the point-slope form, we obtain the equation of the tangent line as y ≈ -1.6829x + 3.2668.

Finally, we substitute x = 1.5 into the equation of the tangent line to approximate f(1.5). After calculation, we find that f(1.5) is approximately 0.0009.

Therefore, the approximation for f(1.5) using the tangent line to the graph at x = 1 is approximately 0.0009.

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Answer:

The exact same

Step-by-step explanation:

^ just means put it up like 3^2=3²

Answer:

It has been answered for you

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Answer:

[tex]M(7 ; 4)[/tex]

Step-by-step explanation:

midpoint -M

[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]

[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]

[tex]M(7 ; 4)[/tex]

Answer:

(7, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then

midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )

Answer:

Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. Multiplying any term of the sequence by the common ratio 6 generates the subsequent term.

Step-by-step explanation:

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please help me

Step-by-step explanation:

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