URGENT DUE TODAY DEC 16
Find the difference between (1.6 × 108) and (8.2 × 107). Write the final answer in scientific notation.


−6.6 × 101

6.6 × 10−1

7.8 × 108

7.8 × 107

Answer:

Step-by-step explanation:

a) The eigenvalues of matrix A are approximately 4.79 and 0.21, with corresponding eigenvectors [1, -1, 2] and [-1, 0.26, -0.26]. b) A diagonal matrix can be obtained using an invertible matrix P, given by [[4.79, 0], [0, 0.21]]. c) Computing A³⁰ is not possible as A is not a square matrix.

(a) To find the eigenvalues and corresponding eigenvectors of matrix A, we need to solve the equation (A - λI)x = 0, where λ represents the eigenvalues and x represents the eigenvectors. Here, A is the given matrix and I is the identity matrix. Let's calculate:

A - λI = 1-λ 1 1 2 4-λ

Setting the determinant of the above matrix equal to zero, we can find the eigenvalues:

(1-λ)(4-λ) - 2(1) = λ² - 5λ + 2 = 0

Solving this quadratic equation, we find the eigenvalues λ₁ ≈ 4.79 and λ₂ ≈ 0.21.

Next, we substitute each eigenvalue back into (A - λI)x = 0 to find the corresponding eigenvectors:

For λ₁ ≈ 4.79:

(A - 4.79I)x₁ = 0

-3.79x₁ + x₂ + x₃ = 0

2x₁ + x₂ + x₃ = 0

One possible eigenvector is x₁ = 1, x₂ = -1, x₃ = 2.

For λ₂ ≈ 0.21:

(A - 0.21I)x₂ = 0

0.79x₁ + x₂ + x₃ = 0

2x₁ + 3.79x₂ + x₃ = 0

Another possible eigenvector is x₁ = -1, x₂ = 0.26, x₃ = -0.26.

(b) To find an invertible matrix P such that P⁻¹AP is a diagonal matrix, we need to construct a matrix P whose columns are the eigenvectors we found. Let P be the matrix formed by these eigenvectors:

P = [1 -1]

   [0.26 0]

   [-0.26 2]

To obtain the diagonal matrix, we compute P⁻¹AP:

P⁻¹AP = [[4.79 0]

          [0 0.21]]

(c) Computing A³⁰ involves raising the matrix A to the power of 30. However, the given matrix A is not a square matrix (3x2), and we cannot raise a non-square matrix to a power. Therefore, we cannot directly calculate A³⁰.

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Answer:

.38, 40%, .59, 6/8

Step-by-step explanation:

convert all to decimal and then order

.38=.38

40%=.40

.59=.59

6/8=.75

Answer:

-61b - 30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

3(-8b - 9b - 10) - 10b

Step 2: Simplify

Answer:

f(x) = \(\sqrt{x}\)

Step-by-step explanation:

hope this helped :-)

The probability of the specific order a, b, c, d, e, f being chosen is approximately 0.0014.

To find the probability of a specific order of performance among the six stand-up comics (a, b, c, d, e, and f), we need to consider the total number of possible orders and the specific order we are interested in.

Since the order of performance is determined by random selection, each comic has an equal chance of being selected first, second, third, and so on. Therefore, the total number of possible orders is given by the factorial of the number of comics (6! = 720) since there are six comics.

Now, let's say we want to find the probability of the order a, b, c, d, e, f. This means that comic a performs first, followed by b, then c, d, e, and finally f.

To calculate the probability, we need to determine the number of favorable outcomes (the specific order we want) divided by the total number of possible outcomes.

In this case, there is only one favorable outcome, which is the specific order a, b, c, d, e, f. Therefore, the number of favorable outcomes is 1.

Thus, the probability of the specific order a, b, c, d, e, f is:

P(a, b, c, d, e, f) = Number of favorable outcomes / Total number of possible outcomes

                      = 1 / 720

                      = 1/720 ≈ 0.0014

Therefore, the probability of the specific order a, b, c, d, e, f being chosen is approximately 0.0014.

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s=m×60

Step-by-step explanation:

where s is the seconds,and m is the minutes

for part b,lets use my formular...

s=m×60=s=30×60=1800,therefore,there are 1800 seconds in 30 minutes.pls mark brainliest.

The probability of a student completing the final examination in less than 65 minutes is 13.45%.

The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).

The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:

Z = (x - μ) / σ

Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.

Plugging these values into the formula, we get:

Z = (65 - 77) / 12 = -1.17

Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.

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Answer:

52

Step-by-step explanation:

26 * 2 = 52

If he does 26 words in one minute, in two minutes he will do twice that.

Have a nice day!

     If this is not what you are looking for - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

52

Step-by-step explanation:

Its just basic math? 26*2=52

Answer: its D

Step-by-step explanation: js trust mee :)

Given

Principal = $2419

rate = 2.54%

time = 7 years

compounds quarterly

After 7 years, the amount deposit is now $2888.08, subtract by the principal amount to get the interest.

Therefore, the interest that he will earn after 7 years us $469.08.

Based on the given options, the correct answer for the confidence interval is:

c. [0.2597, 0.3403]

The confidence interval represents a range of values within which we can estimate the true population parameter with a certain level of confidence. In this case, the confidence interval suggests that the true population parameter falls between 0.2597 and 0.3403.

To calculate a confidence interval, we typically need information such as the sample mean, sample standard deviation, sample size, and a desired confidence level. Without this information, it is not possible to determine the exact confidence interval.

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Answer:

The statement that a 90% confidence interval will have a width of 2.36 based on the given sample mean and population standard deviation is not valid.

Step-by-step explanation:

The width of a confidence interval depends on the confidence level, sample size, and population standard deviation. It is not solely determined by the sample mean. Therefore, we cannot determine the width of a confidence interval based on the sample mean and population standard deviation alone.

To calculate the width of a confidence interval, you would need to know the formula or have information about the sample size and confidence level. Without that information, it is not possible to determine the width of the confidence interval.

Therefore, the statement that a 90% confidence interval will have a width of 2.36 based on the given sample mean and population standard deviation is not valid.

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Answer:

z=4x

=14y10

Step-by-step explanation:

this is the answer

the answer is the c

18,80,82

Answer:

THE ANSWER IS “your net worth”

Step-by-step explanation:

Based on the given CDI and BDI values, investing in Segment 2 would be more advantageous for the brand.

Brand X's growth can be determined by analysing  CDI (Category Development Index) and BDI (Brand Development Index) in two segments, Segment 1 and Segment 2.

Segment 1 has a CDI of 125 and a BDI of 95, while Segment 2 has a CDI of 85 and a BDI of 110. Based on the CDI and BDI values, Segment 2 appears to be a more favourable investment opportunity for the brand because the BDI is higher than the CDI.

CDI is an index that compares the percentage of a company's sales in a specific market area to the percentage of the country's population in the same market area. It provides insights into the market penetration of the brand in relation to the overall population.

BDI, on the other hand, compares the percentage of a company's sales in a given market area to the percentage of the product category's sales in that same market area. It indicates the brand's performance relative to the product category within a specific market.

A higher BDI suggests that the product category is performing well in the market area, indicating a higher growth potential for the brand. Conversely, a higher CDI indicates that the brand already has a strong presence in the market area, implying limited room for further growth.

Therefore, The higher BDI suggests a stronger potential for growth in this market compared to Segment 1, where the CDI is higher than the BDI. By focusing on Segment 2, the brand can tap into the market's growth potential and expand its market share effectively.

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Answer:

 8

x

Step-by-step explanation:

pretend the 8 is a exponent

Answer:

\(x^{8}\)

Step-by-step explanation:

whenever exponents are separated by parentheses, multiply them

example:  \((4x^{3})^2\) = \(4^{2}\)·\(x^{6}\) = 16\(x^{6}\)

Answer:

The answer is 17.

Step-by-step explanation:

Since it's a parallelogram, VY = WX.

Therefore, \(5x + 2 = 6x - 1\).

Solving for x we get: \(x = 3\)

To get the measure of segment WX, substitute \(x = 3\) back into the side \(6x - 1\). Therefore \(6x - 1 = 6(3) - 1 = 17\)

The half-life of Potassium-42 can be calculated using the following formula:

t1/2 = (ln 2) / λ

where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.

Substituting the values given, we get:

t1/2 = (ln 2) / 0.055

t1/2 ≈ 12.6 hours

Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.

It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.

To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:

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Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

Step-by-step explanation:

Intersecting secants theorem:

This statement is True due to the Two Point Postulate.

The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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(3,1) is the coordinates of the center in hyperbola curve.

To find the center of a hyperbola:

Locate the midpoint between the two vertices. The center of a hyperbola is the point that lies in the middle of the transverse axis, which connects the two vertices.

In this scenario, the vertices of the hyperbola are given as (1, 1) and (5, 1).

We know, the x-coordinate of the midpoint is the average of the x-coordinates of the vertices, and the y-coordinate of the midpoint is the average of the y-coordinates of the vertices.

Applying this formula:

x-coordinate of the midpoint = (1 + 5) / 2 = 6 / 2 = 3

y-coordinate of the midpoint = (1 + 1) / 2 = 2 / 2 = 1

Therefore, the coordinates of the center of the hyperbola are (3, 1). This point will serves as the center from which the hyperbola curves in its characteristic shape.

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The area of the field is:

A = (x + 20)y

The length of fence needed is:

x + y + x + 20

(remember that 20 ft are not needed because the building, and y ft are not needed because the river)

We have 1000 ft of fencing, then:

1000 = x + y + x + 20

1000 - 20 = 2x + y

980 = 2x + y

Isolating y from the preceding equation:

y = 980 - 2x

Substituting this into the area equation:

A = (x + 20)(980 - 2x)

Distributing:

At the maximum, the derivative of A with respect to x is zero, then:

Recalling the equation of y and substituting this result:

y = 980 - 2x

y = 980 - 2*235

y = 510

The dimensions are:

length: 255 ft (on the side without the building)

width: 510 ft

Answer:

See below

Step-by-step explanation:

Long side = x

         Other long side = x - 20

short side = y  

Area enclosed = xy

x  +   x -20   + y    = 1000    or y = 1020 -2x    <=====sub into first equation

area = x * ( 1020-2x) =  -2x^2 + 1020x  

         this is a dome shaped parabola  

           max will occur at x = -b/2a = - 1020/ (2 * -2) = 255 ft

  then y =   1020 -2x = 510 ft

(area = xy = 130 050 ft^2 )