find the lowest common multiple of 8 and 6

Answer:

345 yards :)

Step-by-step explanation:

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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For the given Rayleigh distribution with \(f(x)= 2axe^{-ax^{2} }\) , the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

the Rayleigh distribution is characterized by a probability density function (PDF) of the form \(f(x)= 2axe^{-ax^{2} }\), where a > 0. This distribution is used to model the magnitude of a two-dimensional vector whose components are independently and identically distributed Gaussian random variables.

For the Rayleigh distribution with the PDF \(f(x)= 2axe^{-ax^{2} }\) , the expected value (mean) is E[X] = sqrt(pi/(4a)), and the variance is :

Var[X] = (2 - pi/2a²).

Now, let's explain the answer in detail. To find the expected value, we integrate the product of the random variable X and its PDF over the range of possible values:

\(E[x] = \int\limits {(0 to a)x* 2axe^{-ax^{2} }} \, dx\)

By substituting u = -ax², du = -2ax dx, the integral becomes:

E[X] = ∫(0 to ∞) -ueⁿ du

Using integration by parts, we have:

E[X] = [-ueⁿ] - ∫(-eⁿ du)

= \([-xe^{-ax^{2}](0 to a) - \int\limits {0 to a}e^{-ax^{2} }\, dx }\)

The first term evaluates to 0 at both limits. The second term can be rewritten as:

E[X] = ∫(0 to ∞) e⁻ᵃˣ² dx

= √(π/4a) (by evaluating the Gaussian integral)

Thus, the expected value of X is E[X] = sqrt(pi/(4a)).

Next, to find the variance, we use the formula Var[X] = E[X²] - (E[X])². First, we calculate E[X²]:

E[X²] = ∫(0 to ∞) x² * 2axe⁻ᵃˣ²) dx

= ∫(0 to ∞) -x * d(e^(-ax²))

= [-x * e^(-ax²)](0 to ∞) + ∫(0 to ∞) e⁽⁻ᵃˣ²⁾ dx

The first term evaluates to 0 at both limits. The second term is the same as the integral calculated for E[X]. Hence:

= √(π/4a)

Substituting the values into the variance formula:

Var[X] = E[X^2] - (E[X])^2

= (√(π/4a)) - (sqrt(pi/(4a)))²

= (2 - π/(2a²))

Thus, the variance of X is Var[X] = (2 - π/(2a^2)).

Therefore, for the given Rayleigh distribution with f(x) = 2axe⁽⁻ᵃˣ²⁾,

the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

Complete Question:

A random variable X has a Rayleigh distribution if its probability density is given by f(x) = 2oxe or for x > 0, where a > 0. Show that for this distribution 1. Al l vandle has a Rayleigh distribution if its probability density i f(x) = 2axe-ar' for I > 0, where a > 0. Show that for this distribution a) The expected value is b) The variance is o? = (1-5)

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The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

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Answer:

31

Step-by-step explanation:

58 - 27 = 31

The smallest possible value of the seventh term of the sequence is 104 .

A sequence is an ordered group of items in mathematics where repetitions are permitted and order is important.

Let the first two terms of the first sequence be a and b and the first two of the second sequence be c and d.

Computing the seventh term,

we see that 5a + 8b = 5c + 8d.

Note that this means that a and c must have the same value of |8|.

To minimize, let one of them be 0;

We assume that a= 0.

Thus, the smallest possible value of c is 8; and since the sequences are non-decreasing we get d > 8.

To minimize, let d = 8. Thus, 5c + 8d = 40 + 64 = 104.

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The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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Answer:

Step-by-step explanation: To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical compression

40.0*10 is the answer

actually it is 400 but u want in decimal so it is 40.0*10

Answer:

40.0*10

Step-by-step explanation:

have a good day!

Answer:

B is the right answer

Step-by-step explanation:

According to the corresponding angles theorem, the relationship between angles m and n is: C. m = n.

The Corresponding Angles Theorem, also known as the Corresponding Angles Postulate, states that when two parallel lines are intersected by a transversal (a line that crosses both parallel lines), the corresponding angles formed on the same side of the transversal are congruent (equal in measure).

Thus, angles m and n are corresponding angles. Therefore, based on the corresponding angles theorem, the relationship between angles m and n is: C. m = n.

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Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The value of y when x=12 is 600

The values of y vary directly with x

y α x

y = kx

where k is the proportationality constant

The values of y=425 when x=8.5

y = kx

425 = k (8.5)

k = 50

We need to find the value of y when x=12

y = kx

y = 50 x 12

y = 600

Therefore,  the value of y when x=12 is 600

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Answer:

20:25 probably don't quote me

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

48°

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

The derivative of the given function using the Fundamental Theorem of Calculus, Part 1, is -2sinx * cosx.

In mathematics, the derivative of a function of a real variable measures the sensitivity to a change in the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

To find the derivative using the Fundamental Theorem of Calculus, Part 1, for the function \(d/dx(\int_{0}^{(sinx)} (1 - t^2) dt)\), proceed as follows:

1. Identify the function within the integral:

f(t) = 1 - t²
2. Take the derivative of the function with respect to t:

f'(t) = -2t
3. Replace the t variable with the upper limit of the integral, which is sinx:

f'(sinx) = -2sinx
4. Multiply the result by the derivative of the upper limit with respect to x:

d/dx(sinx) = cosx
5. Multiply the results from steps 3 and 4:

-2sinx * cosx

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Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??

The magnetic field B at a distance of 2 cm, 10 cm, and 20 cm away from the axis of a solid wire of radius 10 cm carrying a current of 5.0 A uniformly distributed over its cross-section is 0.01 T, 1.0 x 10^-5 T, and 2.5 x 10^-6 T respectively, and a graph of B versus x for 0 < x < 20 cm shows a peak value of 0.01 T at x = 0 and a rapid decrease to approach zero as x approaches the radius of the wire.

To find the magnetic field B at a point at a distance r from the axis of the wire, we can use the formula:

B = μ₀I/(2πr)

where B is the magnetic field, I is the current, r is the distance from the axis, and μ₀ is the permeability of free space (4π x 10^-7 T m/A).

(a) At a distance of 2 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.02 m)

= 0.01 T

(b) At a distance of 10 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.10 m)

= 1.0 x 10^-5 T

(c) At a distance of 20 cm from the axis, the magnetic field is:

B = μ₀I/(2πr)

= (4π x 10^-7 T m/A) x (5.0 A)/(2π x 0.20 m)

= 2.5 x 10^-6 T

To sketch a graph of B versus x for 0 < x < 20 cm, we can use the formula for B and plot it for different values of x. Since the current is distributed uniformly over the cross-section of the wire, the magnetic field will also be symmetric around the axis of the wire. Therefore, the graph will have a maximum at x=0 and will decrease as x increases.

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Answer:

1. 3/7

2.6/10

3.17/12

4.41/42

5.4/10

6.10/7

hopefully this helped :)

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The rental cost for each movie is $2 and the cost for renting each video game is $2.60.

Here, we have to implement the formation of a quadratic equation to solve the given question.

therefore,

let us call X  the cost of renting a movie and call Y  renting a video game.

in the first month, Omar rented 6 movies along with 2 video games for $24 placing the values to form a quadratic equation,

6X + 2Y = 24 - let this be the first equation

in the second month, Omar rented 3 movies along with 5 video games for $33 placing the values to form a quadratic equation

3X + 5Y = 33 - let this be the second equation

Multiplying the given first equation by -3

-18X - 6Y = -72

now, adding the current first equation to the second equation

-15Y = -39

solving y concerning x

Y = $2.60

placing the value of Y in the first equation gives

X = $2

The rental cost for each movie is $2 and the cost for renting each video game is $2.60.

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The complete question is

One month Omar rented 6 movies and 2 video games for a total of $24 . the next month he rented 3 movies and 5 video games for a total of $33. Find the rental cost for each movie and each video game.

Answer:

There's no expressions.

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Solution

It take 3/4 of a minute -------> 1 lap

3/4 of a minute = 3/4 x 60 = 45secons

Therefore

1 lap = 45 seconds

1/2 hour = 30 min

30 min = 30 x 60 seconds

= 1800 seconds

since

Hence the answer = 40 laps

Answer:

n/2 - 6 + 10

8/2 - 6 + 10

4 - 6 + 10

= 8

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation:

I just took the test, sorry if I didn't come on time.

Answer:

Step-by-step explanation:

Yes, it is possible if the data is skewed negatively and the median is greater than the mean.