boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 12^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 25^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer: 1/\(3^{12}\)

Step-by-step explanation:  \((3^{6} )^{-2}\)

1/ \((3^{6} )^{2}\)  =  1/ \(3^6 . 3^6\)  = 1/ \(3^{12}\)

Review your exponent rules

Multiply powers together when raising a power by another exponent, (a^m)\((a^{m} )^{n}\) = \(a^{m.n}\)

Answer:  0.6

Step-by-step explanation:

Answer:

Postitive numbers

Step-by-step explanation:

Answer:

81%

Step-by-step explanation:

81 out of 100 is 0.81, which is 81%

Hope this helps plz mark brainliest if correct :D

Answer:

0.800

Step-by-step explanation:

Hope it Helps

Answer:

-1

Step-by-step explanation:

Mode is the number that appears most often

−1, 0, 3, 4, −3, −1

-1 appears twice which is more than any other number

-1 is the mode

Suppose dorothy drops a ball from a height of 10 feet. after the ball hits the floor, it rebounds 65% of its previous height.The formula that represents the height of the ball after its nth bounce is given by

\(y = (0.65)^n \times 10 feet.\)

When a ball is dropped from a height of 10 feet, it rebounds to 65% of its previous height each time it bounces.

To find the height of the ball after the nth bounce, we need to use a geometric sequence formula,

which is given by

\(y = ar^n-1,\)

where a is the initial term,

r is the common ratio, and

n is the number of terms.

Here, a = 10 feet,

r = 0.65, and

n is the nth term or

the number of times the ball bounces after it is dropped for the first time.

Therefore, the formula that represents the height of the ball after its nth bounce is given by

\(y = (0.65)^n \times 10 feet.\)

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Answer:

1.9

Step-by-step explanation:

First, we have to put them in order: 0.7, 1.4, 1.8, 1.9, 2.1, 2.4, 2.6. The middle one is 1.9.

Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle , that is

3x + 2x + 6 + 6x - 3 ( simplify by collecting like terms )

= 11x + 3

Given the perimeter = 36 units , then

11x + 3 = 36 ( subtract 3 from both sides )

11x = 33 ( divide both sides by 11 )

x = 3

Then

base = 2x + 6 = 2(3) + 6 = 6 + 6 = 12 units

height = 3x = 3(3) = 9 units

hypotenuse = 6x - 3 = 6(3) - 3 = 18 - 3 = 15 units

Answer:

a

Step-by-step explanation:

from each 100 there is 12

so from x there is 42 and do multible crossing

Answer:

Step-by-step explanation:

putting value

2x - 4(3x) =3

2x- 12x = 3

-10x = 3

If firm issues​ commercial paper with $1000000 face-value and pays EAR of​ 7.4%, then amount the firm will receive is $981500.

To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.

The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.

To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).

Quarterly interest rate = (EAR)/(number of compounding periods)

= 7.4%/4

= 1.85%,

Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,

Interest earned = (face value) × (quarterly interest rate)

= $1,000,000 × 1.85% = $18,500,

So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:

Amount received = (face value) - (interest earned)

= $1,000,000 - $18,500

= $981,500.

Therefore, the amount that firms receives is $981500.

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To create a pattern with exactly 2 lines of symmetry using the given shape and shading in two more squares, follow these steps:

1. Identify the center of the shape, where the lines of symmetry will intersect.
2. Shade in one square on the left side of the center, maintaining equal distance from the center and any existing shaded squares.
3. Shade in another square on the right side of the center, mirroring the position of the square you shaded in step 2.

Now, your pattern will have 2 lines of symmetry: one vertical line going through the center, and one horizontal line going through the center. The symmetry of the pattern is achieved by having equal distribution of shaded squares on both sides of these lines.

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Answer:

I think it's B.

Step-by-step explanation:

:)

Answer:

?????

Step-by-step explanation:

Answer:

wait what?

Step-by-step explanation:

Answer:

Chairs: 1.75   Tables: 8.50

Step-by-step explanation:

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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The dog's total displacement was 8.83 m, and the total distance covered was 13.4 m.

The displacement of an object is represented by an arrow because it has both magnitude and direction.

By using the Pythagorean theorem, the magnitude of the displacement can be calculated.

The total distance is the sum of all the distances covered by the object. The magnitude of the individual displacements is used to calculate the total distance. The total distance and displacement of the dog can be calculated as follows

When calculating the total distance and displacement of the dog, the following diagram can be used. As shown in the diagram, the dog initially runs 2.8 m to the west of its owner and then runs 10.6 m to the east of its owner.

The magnitude of the displacement can be determined using the Pythagorean theorem, which is as follows:

total displacement=√(2.8^2+10.6^2)=√78=8.83 m

The displacement of the dog is 8.83 m.

In this case, the displacement is the vector that represents the dog's movement from its initial position to its final position.

To determine the total distance, the distance covered by the dog in each direction must be calculated and added together. The distance traveled to the west was 2.8 m, while the distance traveled to the east was 10.6 m.

As a result, the total distance covered by the dog is as follows:

total distance=2.8+10.6=13.4 m

As a result, the dog's total displacement was 8.83 m, and the total distance covered was 13.4 m.

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Answer:

\(x \geqslant 1\)

Step-by-step explanation:

The expression in the square root should be greater than or equal to zero, because square root of a negative number does not give a real number.

\(x - 1 \geqslant 0 \\ x \geqslant 1\)

There are 10 members on the board, so there are 10 ways to elect a president, 9 ways to elect a vice president, 8 ways to elect a secretary, and 7 ways to elect a treasurer.

This is because each position can be filled by any of the members, except for the position that the member is already filling. For example, the president can be elected from any of the 10 members, but the vice president must be elected from the remaining 9 members.

The company sea esta has ten members on its board of directors, so it has a lot of different options for how to elect a president, vice-president, secretary, and treasurer. One way to elect a president would be to have the board members vote on who they want to be president.

Another way to elect a president would be to have the members of the company vote on who they want to be president. There are many different ways to elect officers, and it really depends on the company and what they want to do.

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Answer:

1,2,4

Step-by-step explanation:

1: The temperature should be decreasing in an exponential rate as the coffee is hot

2: radioactive element should keep decreasing over years

3: should be increasing rate

4: 'popularity is declining' indicates it's a decay

5: 'growing community' indicated it's increasing

Answer:

Assume that the expression is:

r = √(A)/3

Multiply both sides by 3:

3r = √(A)

Finally, square both sides to get:

A = (3r)²

= 9r²

I hope this helps!

Step-by-step explanation:

The value of a will be 3r².

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The expression is;

r = √a/3

Now,

The expression is;

r = √a/3

Square both sides to get:

r² = a/3

Multiply both sides by 3:

3r² = a

Thus, The value of a will be 3r².

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Answer:

a)

Step-by-step explanation:

Respuesta:

1/6

Explicación paso a paso:

La probabilidad es la probabilidad o probabilidad de que ocurra un evento. Se expresa como;

Probabilidad = Resultado esperado / Resultado total

Dado que la puntuación total de la muestra es 6 (13, 14, 17, 35, 39, 54)

Resultado total = 6

Dado que vamos a encontrar la probabilidad de ganar,

Puntuación ganadora = 54 (solo un resultado)

Resultado esperado = 1

Sustituir

Probabilidad de ganar = 1/6

It looks like given matrices are supposed to be

\(\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}\)

You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:

• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues

• det(A) = determinant of A = product of eigenvalues

(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since

\(\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6\)

\(\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5\)

and

λ₁ + λ₂ = 6   ⇒   λ₁ λ₂ = λ₁ (6 - λ₁) = 5

⇒   6 λ₁ - λ₁² = 5

⇒   λ₁² - 6 λ₁ + 5 = 0

⇒   (λ₁ - 5) (λ₁ - 1) = 0

⇒   λ₁ = 5 or λ₁ = 1

To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.

• For λ = 1, we have

\(\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0\)

With v = (v₁, v₂)ᵀ, this equation tells us that

2 v₁ + 2 v₂ = 0

so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.

• For λ = 5, we would end up with

\(\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0\)

and this tells us

-2 v₁ + 2 v₂ = 0

and it follows that v = (1, 1)ᵀ.

Then the decomposition of A into PDP⁻¹ is obtained with

\(P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}\)

\(D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}\)

where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.

(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if

\(P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}\)

\(D = \begin{bmatrix}i&0\\0&i\end{bmatrix}\)

(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:

\(\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0\)

Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:

det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0

and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.

• For λ = 1,

\(\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0\)

tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.

• For λ = 2,

\(\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0\)

tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.

• For λ = 3,

\(\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0\)

tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.

Then we have A = PDP⁻¹ for

\(P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}\)

\(D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}\)

(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,

• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃   ⇒   λ₂ + λ₃ = 7

• det(A) = 20 = 2 λ₂ λ₃   ⇒   λ₂ λ₃ = 10

and we find λ₂ = 2 and λ₃ = 5.

I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.

• For λ = 2,

\(\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0\)

tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.

• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.

\(\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0\)

This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.

Then A = PDP⁻¹ if

\(P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}\)

\(D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}\)

Answer:

C B D E A

Step-by-step explanation:

The summation of integers with finite integral power (constant for all integers) up to a finite integer can be evaluated. The correct expressions filled would be in the sequence c,b,d,e,a.

Suppose we take the sum of natural numbers (also called positive integers) raised to power 1, 2, and 3, till the nth integer. Then, their sums are given as shown below:

\(S_1 = 1 + 2 + \cdots + n = \sum_{i=1}^n i = \dfrac{n(n+1)}{2}\\\\S_2 =1^2 + 2^2 + \cdots + n^2 = \sum_{i=1}^n i^2 = \dfrac{n(n+1)(n+2)}{6}\\\\S_3 = 1^3 + 2^3 + \cdots + n^3 = \sum_{i=1}^n i^3 = \left[\dfrac{n(n+1)}{2}\\\right]^2\)

For this case, evaluating the rest of the two summations:

\(\sum_{i=1}^n ca_i = ca_1 + ca_2 + \cdots + ca_n = c(a_1 + a_2 + \cdots + a_n)\\\sum_{i=1}^n ca_i = c\sum_{i=0}^n a_i\)

c was not depending on the variable on which summation is done, which was i. Therefore, it can come out directly.

Thus, whenever we get:

\(\sum_x k f(x)\) where k is not depending on the value of x, then we can take it as:

\(\sum_x k f(x) = k\left(\sum_x f(x) \right)\) (using the distributive property of multiplication over addition).

Similarly, we get:

\(\sum_{i=1}^n c = c + c + \cdots + c \text{ (n times)} = c\times n\\\sum_{i=1}^n ca_i = c.n\)

Thus, the summation of integers with finite integral power (constant for all integers) up to a finite integer can be evaluated. The correct expressions filled would be in the sequence c,b,d,e,a.

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Answer:

The number is 8. The recipe calls for 8 ounces of tomatoes per ounce of onions

Step-by-step explanation:

I'm assuming the question you asked goes with a graph, and the only graph I could find with this question came to this answer. Hope this helps?

Answer:

8

Step-by-step explanation: