a rectangele has and area of 48 in every dimension

The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Point-slope form: y - 2 = 3(x - 3)

To find the equation of a line with a given slope and passing through a given point, we use the point-slope form of the equation of a line. In this case, we are given that the slope of the line is 3 and it passes through the point (3,2).

Substituting these values into the point-slope form, we get:

y - 2 = 3(x - 3)

Expanding the right side, we get:

y - 2 = 3x - 9

Adding 2 to both sides, we get:

y = 3x - 7

This is the slope-intercept form of the equation of the line. The slope-intercept form is useful because it gives us information about both the slope and y-intercept of the line. In this case, we know that the slope is 3 and the y-intercept is -7.

We can use the slope-intercept form to graph the line or to find other points on the line. For example, if we want to find the x-intercept of the line, we can set y = 0 and solve for x:

0 = 3x - 7

Adding 7 to both sides, we get:

7 = 3x

Dividing both sides by 3, we get:

x = 7/3

So the x-intercept of the line is (7/3,0).

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Given that the production function of a firm is f(x1, x2) = x1^(1/3) * x2^(2/3), where price of x1 = 1 and price of x2 = 2. Let's derive the conditional demand for x1 and cost function c(y).

Conditional demand for x1 can be derived as:

∂f(x1, x2)/ ∂x1 = (∂/∂x1) (x1^(1/3) * x2^(2/3))= (1/3) * x1^(-2/3) * x2^(2/3)

Now, put the value of x2 = (y/ x1^(1/3))^3 in the above equation.

∂f(x1, x2)/ ∂x1 = (1/3) * x1^(-2/3) * (y/ x1^(1/3))^2 = (1/3) * y^2 * x1^(-4/3)

Since price of x1 = 1, the cost function can be written as c(y) = w1 * x1 + w2 * x2 = x1 + 2x2 = x1 + 4(y/ x1^(1/3))

The cost function of the firm is

c(y) = x1 + 4y^(1/3) * x1^(-1/3) = x1 + 4y^(1/3)/x1^(1/3)

In order to maximize the profit, we need to differentiate the cost function with respect to x1 and equate it to zero.

(c(y))/d(x1) = 1 - 4/3 * y^(1/3) * x1^(-4/3) = 0

x1 = (3/4) * y^(1/3)

On substituting the value of x1 in the cost function, we get:  

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Answer:

10

Step-by-step explanation:

according to the formula of y = P(1-r)^x, P is the initial value, and in this case it looks like it is 10 :)

The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .

What is a Boolean Expression ?

The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.

Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .

If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .

The given question is incomplete , the complete question is

What is Dual Boolean Expression ?

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Step-by-step explanation:

Given that,

The area of a blackboard is \(1\dfrac{1}{3}=\dfrac{4}{3}\ \text{yards}^2\)

The area of poster is \(\dfrac{8}{9}\ \text{yards}^2\)

We need to find the unit rate of the blackboard's area to the poster's area. So, it can be calcualted by dividing blackboard's area to the poster's area.

So,

\(\dfrac{\dfrac{4}{3}}{\dfrac{8}{9}}=\dfrac{4}{3}\times \dfrac{9}{8}\\\\=1.5\)

So, the rate of \(1.5\ \text{yard}^2\).

Answer:

x=22.5°

Step-by-step explanation:

(cos²x-sin²x)-sin4x+sin²2x=0

or, (cos2x)²-sin4x+sin²2x=0

or, cos²2x+sin²2x-sin4x=0

or, 1-sin4x=0

or, sin4x=1

or, 4x=90°

or, x=90°/4

or, x=22.5°

Step-by-step explanation:

AC = 20

AB = 18

BC² = 20²+ 18² -2•20•18•cos(52°)

BC² = 280.72

BC = √280.72

BC ≈ 16.75

Angle C:

18² = 20² + 16.75² -2•20•16.75•cos(C)

324 = 400 + 280.72 -670•cos(C)

cos(C) = -356.72/-670

cos(C) ≈ 0.53

acos(0.53) = C

C = 57.8°

Angle B:

180-52-57.8 = 70.2°

Answer:

q = -150

Step-by-step explanation:

-q/5 = 30

Multiply each side by 5/1 to get -q by itself:

-q = 150

Because there is a negative sign in front of the q, you need to multiply both sides by -1, to get only q on one side:

q = -150

Answer:

q= -150

Step-by-step explanation:

30*5=150 and since there is a negative sign in front of the q, 150 has to be negative for the answer to be positive.

Answer:

A) Cube

Explanation:

Quadrilateral just means "four sides"

Examples: square, rhombus, parallelogram, rectangle.

Hope that helps

Answer:

-6

Step-by-step explanation:

is that quizzes join lol

i think its 50 u need to multiply √5 *√5 that is 5

Answer:

10

Step-by-step explanation:

The square root of the number 100 is 10.

I hope it helps! Have a great day!

Anygays-

Answer:

10

Step-by-step explanation:

The answer should be 10 because he square root of the number 100 is 10.

I hope it helps! Have a great day!

Pan~

The ''Solid C'' shows the least surface area.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

These solids all have the same volume.

Now, All the shapes are shown in figure.

Hence, We know that;

In all shapes solid C shows the shape of sphere which have least surface area.

Thus, The ''Solid C'' shows the least surface area.

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The integral of 4f(2x)dx from 0 to 1 is 5.

To find the integral of 4f(2x)dx from 0 to 1 when given that f is continuous and the integral of f(x)dx from 0 to 8 is 10, follow these steps:

1. Make a substitution: Let u = 2x, so du/dx = 2 and dx = du/2.

2. Change the limits of integration: Since x = 0 when u = 2(0) = 0 and x = 1 when u = 2(1) = 2, the new limits of integration are 0 and 2.

3. Substitute and solve: Replace f(2x)dx with f(u)du/2 and integrate from 0 to 2:
  ∫(4f(u)du/2) from 0 to 2 = (4/2)∫f(u)du from 0 to 2 = 2∫f(u)du from 0 to 2.

4. Use the given information: Since the integral of f(x)dx from 0 to 8 is 10, the integral of f(u)du from 0 to 2 is (1/4) of 10 (because 2 is 1/4 of 8). So, the integral of f(u)du from 0 to 2 is 10/4 = 2.5.

5. Multiply by the constant factor: Finally, multiply 2 by the integral calculated in step 4:
  2 * 2.5 = 5.

Therefore, the integral of 4f(2x)dx from 0 to 1 is 5.

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The remainder of the polynomial equation is -49

The remainder of a quantity in an algebraic expression of a polynomial equation is the remaining amount of the quantity left and can not be divisible by the divisor.

From the given information, we are to find the remainder of the given algebraic equation:

\(\mathbf{= \dfrac{5x^3+7x+5}{x+2} }\)

Using the long division method, we have:

\(\mathbf{= \dfrac{5x^3+7x+5}{x+2} } \implies \mathbf{5x^2 + \dfrac{-10x^2+7x+5}{x+2}}\)

Divide by \(\mathbf{ \dfrac{-10x^2+7x+5}{x+2}}\), we have:

\(\mathbf{= 5x^2- 10x+ \dfrac{27x+5}{x+2}}\)

Divide by \(\mathbf{\dfrac{27x+5}{x+2}}\), we have:

\(\mathbf{= 5x^2- 10x+ 27 +\dfrac{-49}{x+2}}\)

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Answer:

2/15

Step-by-step explanation:

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

∠BEF

Step-by-step explanation:

Angle BEF is connected by the three line segments, and does not break apart. They are a straight line, and do not jump across the picture to connect to another point.

Answer:

BEF

Step-by-step explanation:

Bef makes a obtuse angle

10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Answer:  -3x+5y=-2 = x=5/3y+2/3  

3x+7y=26 = x=-7/3y+26/3

Step-by-step explanation:

Answer:

A (4,2)

Step-by-step explanation:

edge

Answer:

How are you? 1

Step-by-step explanation:

Answer:

98.01

Step-by-step explanation:

\([9.9]^2\\=[\frac{99}{10}]^2\\ =\frac{9801}{100}\\ =98.01\)

Answer:

12t - 1

Step-by-step explanation:

(9t+5) + (3t-6)

9t + 5 + 3t - 6

12t - 1

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer:

18/25

Step-by-step explanation:

i dont have an explanation

Answer:

525

Step-by-step explanation:

i really dont know what it asking