please show all the work

For #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2

okjajsjajajamaakqkaka

Answer:

Is this helpful or wrong?

Answer:

hey there, the product is x³ - 1

The sampling distribution of the sample mean I, when n = 8, is approximately normal with a mean of 22.4 and a standard deviation of approximately 0.74375.

(a) The sampling distribution of the sample mean, denoted by I, when n = 8 from a population with a left-skewed distribution of mouse lifespans can be described as approximately normal. According to the central limit theorem, as the sample size increases, the sampling distribution of the sample mean tends to follow a normal distribution regardless of the shape of the population distribution, given that certain conditions are met.

(b) The mean of the sampling distribution of the sample mean, denoted as H(I), is equal to the mean of the population, which is 22.4. This means that, on average, the sample means obtained from samples of size 8 will be centered around 22.4.

(c) The standard deviation of the sampling distribution, denoted as σ(I), is equal to the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 2.1, and the sample size is 8. Therefore, the standard deviation of the sampling distribution is 2.1 divided by the square root of 8, which is approximately 0.74375.

In summary, the sampling distribution of the sample mean I, when n = 8, is approximately normal with a mean of 22.4 and a standard deviation of approximately 0.74375.

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Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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Answer:

10:20 A.M.

Step-by-step explanation:

The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.

Let's say there are "m" appetizer options and "n" vegetable options on the menu.

Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:

m x n ways

So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.

Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.

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If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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False. An n × n matrix that is orthogonally diagonalizable does not necessarily have to be symmetric. A matrix is said to be orthogonally diagonalizable if it can be expressed as PDP^T, where P is an orthogonal matrix and D is a diagonal matrix.

For a matrix to be symmetric, it must satisfy the condition A = A^T, where A^T denotes the transpose of A. While it is true that symmetric matrices are always orthogonally diagonalizable, the converse is not necessarily true. There exist non-symmetric matrices that can still be orthogonally diagonalized. An example of such a matrix is the following:

  [1  2]

A = [3 4]

This matrix is not symmetric, as A^T is:

  [1  3]

A^T = [2 4]

However, it is still orthogonally diagonalizable. The matrix A can be diagonalized as:

A = PDP^T, where P = [0.8507 -0.5257]

[0.5257 0.8507]

          and D = [-0.3723   0     ]

                    [ 0      5.3723]

Therefore, it is not necessary for an n × n matrix that is orthogonally diagonalizable to be symmetric.

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The perimeter of the figure is 53.7.

Perimeter can be defined as the total distance around a object.

To calculate the perimeter of the the figure below, we use the formula below.

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the perimeter of the figure is 53.7

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HOPE THIS HELPS!!!!!!!!!!!!!! :)

Answer:

Yes and no, with the amount of dirt there is most of it would fit in the 20 buckets but there are still 0.2 pounds of dirt left.

Step-by-step explanation:

2.56x = 51.78

Divide

x = 20.2

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Answer:

Standard Form:-w^12+4w^11

Degree: 12 degree

Leading Coefficient: -1

Step-by-step explanation:

Standard Form: Order the exponents from greatest to least.  

Degree: The largest exponent is the degree; the exponent in the first term, IF it is in standard form.

Leading Coefficient: The coefficient of the first term in standard form.  There is and understood 1 before the w in the first term.

The required answers are given below,

Standard Form:-w¹²+4w¹¹

Degree: 12 degree

Leading Coefficient: -1

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Standard Form: Order the exponents from greatest to least. The largest exponent is the degree; the exponent in the first term, IF it is in standard form.

Leading Coefficient: The coefficient of the first term in standard form. There is an understood 1 before the w in the first term.

The answers are given as below,

Standard Form:-w¹²+4w¹¹

Degree: 12 degree

Leading Coefficient: -1

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Answer:

A = 147°

B = 33°

Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.

Given that:

Amount he spends = $94

His base salary = $79/ month

Additional amount = $ 3

Let x represents the money he earn for every one class.

we can no put it in a equation:

   79(1) + 3x = 94

⇒ 79 +3x = 94

⇒ 3x = 15

⇒ x = 15/3

⇒ x = 5

Therefore, Lorenzo will take 4 classes total in first month. Also, his expense will be $15 and earning will be $79.

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The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

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Answer:

see explanation

Step-by-step explanation:

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

y = x² - 4x - 1

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(-2)x + 4 - 4 - 1

y = (x - 2)² - 5

with vertex = (2, - 5 )

Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Answer:18.4

Step-by-step explanation:add

Answer:

1. No Solution

2. Infinity solutions

3. One Solution

Step-by-step explanation:

1.   2x-3=2(x-1)

distribute the 2

2x - 3 = 2x - 2

2x cancels out

-3 ≠ -2

therefore no solution

2. 3(x - 4) = 2x - 9 +x - 3

distribute and add common factors

3x - 12 = 3x - 12

3x cancels out

-12 = -12

Therefore infinity solutions

3. 2(2x + 3) = 2(3x + 2)

distribute

4x + 6 = 6x + 4

minus 6x

-2x + 6 = 4

minus 6

-2x = -2

There for x=1 meaning one solution

Answer:

I have to say this problem is poorly worded.

the answer they're looking for is 8, I believe.

they defined t(x) twice!

Answer:

diabetes is the correct answer tehehehe

Answer:

he now has 120 candy bars

Step-by-step explanation:

After 1st Translation  (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)

What is translation?

And image After Composition means resultant image after you plot the translated points.

So, Given Vertices are X(2,4), Y(6,0), Z(7,2)

Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)

After 2nd Translation = X(4,11), Y(8,7), Z(9,9)

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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?

The function f(d(x))=9/5|x^100|+32 shows the composition (d(x).

The function d(x) calculates how many degrees a container of water at temperature x is away from boiling water. It accepts a value of x in degrees centigrade. The formula f(d) converts a value in degrees Celsius, d, into a value in degrees Fahrenheit, d(x). As a result, when we do f(d(x)), we are integrating d(x) into f. (d).

The domain of f(d(x)) is now the range of d(x). This means that the function f(d(x)) displays the number of degrees Fahrenheit that a water container is away from the boiling point of water at a temperature x in degrees Celsius.

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Answer:

Here is a picture of a right trapezoid with bases of 8 and 10 cm

Answer:

Below

Step-by-step explanation:

Circumference = pi * d = 22/7 * d

2517 = 22/7 * d             ( are you sure 2517 is correct??)

d = 2517 * 7/22 = 800.86 inches    ( a VERY large pie)

radius = 1/2 * d = 400.43 inches

Area = pi r^2

        = 22/7   * (400.43)^2 = 503 943 in^2

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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