What is the range of this function?

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Answer:

How to Answer, “Tell Me About a Time You Went Above and Beyond”

First, describe the situation you were in.Then, explain the task at hand, or the challenge you had to overcome.Next, explain the action or plan you chose and why.

Step-by-step explanation:

When going in for that all important job interview, your goal is to sell yourself as the most qualified for the job. Answering the interview questions with knowledgeable and detailed answers is the best strategy to do that. Most job interviews follow a somewhat predictable format of questioning. In general, interview questions are either traditional, which are closely related to the line of work or your specific experiences, or behavior based. Behavioral interview questions are the ones that make many job applicants nervous, with questions such as ‘Talk about a time when communications broke down and the person you were talking with misunderstood you.’

Answer:

C

Step-by-step explanation:

-4(2p + 5) + 8p = -11

-8p - 20 + 8p = -11

-8p + 8p = -11 + 20

-8p+8p will give you zero and our aim is to find the value of p. Since p has already be eliminated, there's no need going further. So my answer is C.

The equation has no solution.

Using location of points and a system of equations, it is found that:

----------------------------------

Point C is located between points B and D means that:

\(BD = BC + CD\)

----------------------------------

We are given that:

From this, two equations can be built.

\(2x + 8y = 38\)

Dividing both sides by 2:

\(x + 4y = 19\)

\(x = 19 - 4y\)

----------------------------------

Finding y:

\(BC + CD = BD\)

\(5x + 7 + 3y + 4 = 38\)

\(5x + 3y + 11 = 38\)

\(5x + 3y = 27\)

Since \(x = 19 - 4y\)

\(5(19 - 4y) + 3y = 27\)

\(95 - 20y + 3y = 27\)

\(17y = 68\)

\(y = \frac{68}{17}\)

\(y = 4\)

----------------------------------

Finding x:

\(x = 19 - 4y = 19 - 4(4) = 19 - 16 = 3\)

The value of x is 3.

The value of y is 4.

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Answer:

Turn one of the plus signs into a 4, making it 545+5=550

Step-by-step explanation:

Answer:

m∠CBD = 55°

Step-by-step explanation:

Angles BDA and BDC form a linear pair:

⇒ m∠BDA + m∠BDC = 180°

⇒ 80° + m∠BDC = 180°

⇒ m∠BDC = 100°

Interior angles of a triangle sum to 180°:

⇒ m∠CBD + m∠BDC + m∠DCB = 180°

⇒ m∠CBD + 100° + 25° = 180°

⇒ m∠CBD + 125° = 180°

⇒ m∠CBD = 55°

Answer:

Step-by-step explanation:

h(t) = - 16t² + 22t + 6

h = 13.5625 ft

I think it would be the red line its going to be Negative

around 0 to 2

Answer:

Arc length = 7.33 inches

Step-by-step explanation:

The formula for arc length is s = rθ, where s = arc length, r = radius, and θ is the central angle in radians.

We are given that the radius is 7, and the central angle is 60 degrees, which means we have to convert the central angle to radians and then plug in the values to solve:

π radians = 180 degrees

60 degrees * (π radians/180 degrees) = π/3 radians

r = 7;  θ = π/3

s = 7*π/3

s = 7π/3

s = 7.33

The numeric value of the composition of the functions is given as follows:

f ( g ( f ( f ( f ( g ( 27 ) ) ) ) ) ) = 1.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The functions for this problem are given as follows:

We obtain the numeric values from the inside out, hence:

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Answer:

2.85 divided by 2.91 is 0.97938144329

so about 97.9 percent 2.1 percent decrease

Answer:

2.1

Step-by-step explanation:

put change over original times percent over 100

so .06 times 100 is 6 and 6 divided by 2.91 is 2.06 and rounding to the nearest tenth would be 2.1%

Using the principle of proportional relationship, the length of hair grown by the dog in 1 week would be 0.2 inches

Setting up the relationship thus :

12.5 weeks = 2.5 inches

1 week = p inches

Cross multiply

12.5p = 2.5

Divide both sides by 12.5

p = 2.5 / 12.5

p = 0.2 inches

Hence, the length grown in 1 week is 0.2 inches

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the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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Answer:

12 inches

Step-by-step explanation:

if it is a square then you do 3×4 to get the perimeter

The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = \(\frac{495+500+505+500}{4} = \frac{2000}{4}\)

                                                = 500 hours

Mean service life of sample 2 =\(\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}\)

                                                  = 515 hours

Mean service life of sample 3 =  \(\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}\)

                                                  = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = \(\frac{500+515+470}{3}=\frac{1485}{3}\)

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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The mean of the sampling distribution of sample means is 495 hours.

What is the mean of the samples?

The mean of samples is the average of a set of samples or data.

This can be calculated using the formula:

Mean= (Sum of terms)/(Number of terms)

Find the mean of each sample as shown below:

Mean service life of sample 1 = \(\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}\)

                                               = 500 hours

Mean service life of sample 2 = \(\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}\)

                                                 = 515 hours

Mean service life of sample 3 =  \(\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}\)

                                                 = 470 hours

Find the mean of the sampling distribution of sample means using the formula:

Mean of the sampling distribution (M)

=(Sum of mean of given samples )÷( Number of samples)

M = \(\frac{500+515+470}{3}=\frac{1485}{3}\)

M=495 hours

So, the mean of the sampling distribution of sample means is 495 hours.

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Answer:

Functions

Step-by-step explanation:

ok so you gotta substitute x into the original then expand simplify collect like terms then your done

Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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Answer:

I think it is 30 degrees.

Step-by-step explanation:

Answer:

c is the answer

Step-by-step explanation:

The simplified form of the expression 3(w +1) + 4(2w0 + 3) is 3w + 8w0 + 15.

Simplification is the process of reducing or expressing a complex expression or equation in a simpler form. In mathematics, simplification is often used to make calculations easier, to find solutions to problems, or to gain a better understanding of a mathematical concept. Simplification involves the use of various algebraic properties and techniques to transform an expression into an equivalent, but simpler, form. These techniques include combining like terms, factoring, expanding, using the distributive property, and simplifying fractions, among others. The goal of simplification is to make a mathematical expression or equation more manageable and easier to work with.

To simplify the expression 3(w +1) + 4(2w0 + 3), we need to use the distributive property and simplify the terms as follows:

3(w +1) + 4(2w0 + 3) = 3w + 3 + 8w0 + 12 (distributing 3 and 4)

= 3w + 8w0 + 15 (combining like terms)

Therefore, the simplified form of the expression 3(w +1) + 4(2w0 + 3) is 3w + 8w0 + 15.

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(a) The solutions for x* and y* are given by equations (6) and (7), respectively. (b) When I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

(a) To solve for x* and y* in terms of Pₓ, Pᵧ, and I, we need to find the utility-maximizing bundle that satisfies the budget constraint.

The utility function is given as U(x, y) = x^(1/2) * y^(1/2).

The budget constraint is expressed as Pₓ * x + Pᵧ * y = I.

To maximize utility, we can use the Lagrange multiplier method. We form the Lagrangian function L(x, y, λ) = U(x, y) - λ(Pₓ * x + Pᵧ * y - I).

Taking the partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = (1/2) *\(x^(-1/2) * y^(1/2)\)- λPₓ = 0   ... (1)

∂L/∂y = (1/2) *\(x^(1/2) * y^(-1/2)\) - λPᵧ = 0   ... (2)

∂L/∂λ = Pₓ * x + Pᵧ * y - I = 0               ... (3)

Solving equations (1) and (2) simultaneously, we find:

\(x^(-1/2) * y^(1/2)\)= 2λPₓ   ... (4)

\(x^(1/2) * y^(-1/2)\)= 2λPᵧ   ... (5)

Dividing equation (4) by equation (5), we have:

\((x^(-1/2) * y^(1/2)) / (x^(1/2) * y^(-1/2))\) = (2λPₓ) / (2λPᵧ)

y/x = Pₓ/Pᵧ

Substituting this into equation (3), we get:

Pₓ * x + (Pₓ/Pᵧ) * x - I = 0

x * (Pₓ + Pₓ/Pᵧ) = I

x * (1 + 1/Pᵧ) = I

x = I / (1 + 1/Pᵧ)        ... (6)

Similarly, substituting y/x = Pₓ/Pᵧ into equation (3), we get:

Pᵧ * y + (Pᵧ/Pₓ) * y - I = 0

y * (Pᵧ + Pᵧ/Pₓ) = I

y * (1 + 1/Pₓ) = I

y = I / (1 + 1/Pₓ)        ... (7)

Therefore, the solutions for x* and y* are given by equations (6) and (7), respectively.

(b) Given I = $24, Pₓ = $4, and Pᵧ = $2, we can substitute these values into equations (6) and (7) to find the values of x* and y*.

x* = 24 / (1 + 1/2) = 16

y* = 24 / (1 + 1/4) = 20

So, when I = $24, Pₓ = $4, and Pᵧ = $2, the optimal values of x* and y* are x* = 16 and y* = 20, respectively.

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Suppose U(x,y)=x  1/2  y  1/2  and P  x ​  x+P  y ​  y=I a. Solve for x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I). b. What are the values of x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I) if I=$24,P  x ​  =$4 and,P  y ​  =$2?

Answer:

y=(x-8)(x+6)

Step-by-step explanation:

8 is a factor of 2, 6 adds up to 48

(also, my calculator can factor :P)

Hope this helps!

Answer:

y = (x - 8)(x + 6)

Step-by-step explanation:

In order to turn this into factored form, you need to find which two numbers add to -2 and multiply to -48. First, identify factors and see which ones have a difference of 2:

2 × 24

3 × 16

4 × 12

6 × 8

6 and 8 have a difference of 2 and multiply to 48. In order for them to add to -2 and multiply to -48 though, one must be negative. You can tell that 8 will be negative because -8 + 6 = -2 and -8 × 6 = -48.

At this point, you can write the factored form:

y = (x - 8)(x + 6)

(If you want to check your answer, you can just multiply the binomials using FOIL and see if they are the same as the given quadratic function)

The answer is B) (x² + 3x) (x² + 4x).

What is polynomial?

A polynomial is an expression made up of variables (also known as indeterminates) and coefficients that includes only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The factored form of the polynomial can be found by identifying the factors of each group of tiles and writing the expression in factored form. From the diagram, we can see that:

(x² + 3x) = x(x + 3)

(x² + 4x) = x(x + 4)

Therefore, the polynomial in factored form is:

A(x² + 3x)(x² + 4x) + 6 = A(x(x + 3))(x(x + 4)) + 6 = A(x + 3)(x + 4)x² + 6

So the answer is B) (x² + 3x) (x² + 4x).

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Answer:

y = 1x - 1

Step-by-step explanation:

\(\frac{y2-y1}{x2-x1}\\\frac{1-(-4)}{2-(-3)}\\\frac{1+4}{2+3}\\\frac{5}{5}=1\\y=1x+b\\1=1(2)+b\\1 = 2 + b\\-1 = b\\y = 1x-1\)

Answer: -8/21

Step-by-step explanation:

-5/7= -15/21

1/3=7/21

-15/21+7/21= -15+7=18

(15-7=8)

-8/21

Simplified Solution:

\(-\frac{8}{21}\)

Hope this helps!

Answer:

it should be the negative repirocal of -2 so 1/2

Answer:

mPerpendicular= 1/2

Step-by-step explanation:

Answer:

n has to be negative

Step-by-step explanation:

To solve this equation, 15 has to be subtracted from 2 which is negative

Since n is positive then the overall result will be negative