Hey you come help me please

Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

Answer:

  5.806 × 10³

Step-by-step explanation:

Put a decimal point to the right of the left-most digit: 5.806. Now multiply by the place value of that digit.

  5.806 × 10³

___

The 5 is in the "thousands" place. Of course a "thousand" is 1000 = 10·10·10 = 10³. The place value multiplier (1000 or 10³) is written using the exponent when we write scientific notation.

Answer: 'A' is 3.2 and 'B' is 6.

Autocorrelation function of y(t) is Ry(τ) = E[y(t)y(t+τ)] = (1/2)Rx(τ)cos(w0τ) and power spectral density of y(t) is equal to Sy(w) = (1/2)Sₓ(w-w0) + (1/2)Sₓ(w+w0).

Autocorrelation function of y(t) is calculated E[y(t)y(t+τ)]

y(t)y(t+τ) = x(t)cos(w0t+q) x(t+τ)cos(w0(t+τ)+q)__(1)

We know,

cos(A +B) = cos(A)cos(B) - sin(A)sin(B)

Apply formula in(1) we get,

y(t)y(t+τ) = x(t)x(t+τ)cos(w0t+q)cos(w0τ) - x(t)x(t+τ)sin(w0t+q)sin(w0τ)

x(t) and q are independent.

Taking the expected value of both sides we get,

⇒E[y(t)y(t+τ)] = E[x(t)x(t+τ)]E[cos(w0t+q)cos(w0τ)] - E[x(t)x(t+τ)]E[sin(w0t+q)sin(w0τ)]

Expected value of cos(w0t+q)cos(w0τ) is equal to

E[cos(w0t+q)cos(w0τ)] = E[cos(w0t)cos(w0τ)cos(q) - sin(w0t)sin(w0τ)cos(q)] __(2)

As q is uniformly distributed over the range 0 < q < 2p

Expected value is equal to,

E[cos(q)]

=\(\int_{0}^{2\pi}\) cos(q) * 1/(2p) dq

= 0

Also, E[sin(q)] = 0

E[cos(q)sin(q)] = 0

Substitute in (2) we get,

E[cos(w0t+q)cos(w0τ)] = E[cos(w0t)cos(w0τ)] = (1/2)cos(w0τ)

Similarly,

E[sin(w0t+q)sin(w0τ)] = (1/2)cos(w0τ).

Substituting these values into the expression for E[y(t)y(t+τ)],

⇒E[y(t)y(t+τ)] = (1/2)Rx(τ)cos(w0τ)

Autocorrelation function of y(t) is equal  to,

Ry(τ) = E[y(t)y(t+τ)] = (1/2)Rx(τ)cos(w0τ)

Fourier transform of the autocorrelation function is the power spectral density .

Power spectral density of y(t),

Sy(w) = Fourier[Ry(τ)]

        = Fourier[(1/2)Rx(τ)cos(w0τ)]

Apply cos(A +B) = cos(A)cos(B) - sin(A)sin(B)

cos(w0τ) as the real part of exp(jw0τ).

Substituting this into Ry(τ),

Ry(τ) = (1/2)Rx(τ)Re[exp(jw0τ)]

Taking the Fourier transform of both sides,

Sy(w) = (1/2)Sₓ(w-w0) + (1/2)Sₓ(w+w0)

Therefore, autocorrelation function of y(t) is Ry(τ) = E[y(t)y(t+τ)] = (1/2)Rx(τ)cos(w0τ) and the power spectral density of y(t) is a sum of two shifted copies of the power spectral density of x(t), with peaks at w0 and -w0.

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Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

The solution for 3 on the interval [0, 2) is 3 = π/6, 13π/6 or 30°, 390°.

To solve for 3 from sin(3) = 1/2 on the interval [0, 2), we need to use the inverse sine function (arcsin) and solve for the angle whose sine is equal to 1/2.
arcsin(1/2) = 30° or π/6 radians
Since the interval is [0, 2), we need to add 2π to the angle if it is less than 0 or greater than or equal to 2π.
So, the solution for 3 on the given interval is:
3 = π/6 or 30°, or
3 = π/6 + 2π = 13π/6 or 390°
Therefore, the solution for 3 on the interval [0, 2) is 3 = π/6, 13π/6 or 30°, 390°.

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The volume of the rectangular box is given by using the Lagrangian multiplier theorem is 172.435 cubic units.

It states that any local maxima or any local minima of the function are calculated under the equality constraints.

The equation of ellipsoid is given as,

\(\frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} =1\)

Let the edges of the required rectangular box be x, y, and z.

Then, the volume of the box in the first quadrant is V = xyz

Then we have,

\(\phi(x,y,z) = \frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} -1\)  

By the Lagrange multiplier,

\((V_x,V_y,V_z) = \lambda (\phi_x, \phi_y,\phi_z)\\\\(yz,xz,xy)=\lambda(\frac{2x}{4},\frac{2y}{64},\frac{2z}{49} )\\\\xyz = \lambda\frac{x^2}{2},xyz =\lambda\frac{y^2}{32} ,xyz=\lambda\frac{2z^2}{49} \\\\x^2 = 2k, y^2=32k,z^2=49k/2\)

Solving for k we have the value of k as k = 2/3.

Put k=2/3 in equation 2, we have

x² = 2*2/3 , y² = 32*2/3, z² = 49/2*2/3

x =±2/√3 , y= ±8/√3 , z = ±7/√3

Then the volume of the rectangular box will be

Volume  = \(\frac{2}{\sqrt{3} } \frac{8}{\sqrt{3} } \frac{7}{\sqrt{3} }\)

Volume  = 172.435 cubic units.

Therefore, the value of  volume of the rectangular box is  172.435 cubic units.

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We know that all three terms are important in supervisory experience, but "content" is one that is more crucial than the others

The terms mentioned in your question are "content", "loaded", and "important". In the context of supervisory experience, these terms refer to the quality and quantity of information and tasks assigned to subordinates.

"Content" refers to the information and tasks that are communicated by the supervisor to the subordinate. This includes instructions, feedback, and guidance on how to perform tasks effectively.

"Loaded" refers to the amount of information and tasks that are assigned to subordinates. This can be overwhelming if the workload is too heavy, which can lead to stress and burnout.

"Important" refers to the significance of the information and tasks assigned to subordinates. This relates to the impact that these tasks have on the overall success of the team or organization.

When it comes to supervisory experience, all three terms are important. However, the term "content" is one that is more important than the others. This is because the quality of information and guidance provided by the supervisor has a significant impact on the subordinate's ability to perform tasks effectively. A lack of clear guidance can result in confusion, mistakes, and delays in completing tasks.

The amount of information and tasks assigned to subordinates also has an impact on the supervisory experience. If the workload is too heavy, it can lead to stress and burnout, which can negatively impact job performance. Therefore, supervisors need to balance the workload to ensure that subordinates are not overwhelmed.

The significance of the information and tasks assigned to subordinates also plays a crucial role in supervisory experience. If tasks are not important or relevant, subordinates may feel demotivated or disengaged. Therefore, supervisors need to ensure that tasks are aligned with the team's goals and contribute to the overall success of the organization.

In terms of the subordinate's experience, all three terms play a critical role. Clear and concise instructions (content) can help subordinates perform tasks effectively. A balanced workload (loaded) can help subordinates manage their time and reduce stress. Assigning important tasks (important) can help subordinates feel valued and motivated to contribute to the team's success.

In conclusion, all three terms are important in supervisory experience, but "content" is one that is more crucial than the others. Providing clear guidance and instructions can help subordinates perform tasks effectively, which ultimately leads to team success.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

Fraction: 3/20

Decimal: 0.35

Step-by-step explanation:

a) 100% - 35% = 65

   So, 65% of the houses are NOT blue.

..............................................

Fraction: 3/20

Decimal: 0.35

Answer:

65/100 or 0.65

Step-by-step explanation:

To answer this problem all you have to do is subtract 35%.If an A+ is an 100 percent,Then subtract 100 and 35 giving you 65 percent.

But if you do not know how to turn a fraction or decimal,then i will show you.every time you have a number in the tens place,add a zero and the add the decimal and finally add 65 which making look like this:0.65.

Fraction is easy to do as long as you do a number out of 100,like this:65/100.

simple :)

Answer:

\(area = \frac{45}{360} \times \pi {(15)}^{2} \\ = 88.35729338221 \\ = 88.6 \: (3sf)\)

The function h(x) = 0.0065x – 1.25 represents the sum of the flight time lengths of two airplane flights.

To find the sum of the flight time lengths represented by the functions f(x) and g(x), we need to multiply the functions together. Given f(x) = 0.0025x^0.75 and g(x) = 0.004x^0.5, the function h(x) = f(x) * g(x) represents the sum.

Multiplying the functions:

h(x) = (0.0025x^0.75) * (0.004x^0.5)

Simplifying the expression:

h(x) = 0.0025 * 0.004 * x^0.75 * x^0.5

h(x) = 0.0065x^1.25

Therefore, the function h(x) = 0.0065x – 1.25 represents the sum of the flight time lengths of the two airplane flights.

Understanding how to multiply functions and simplify the resulting expression allows us to determine the correct function that represents the sum. By multiplying the functions f(x) and g(x) together, we obtain the function h(x), which represents the desired sum of the flight time lengths.

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Answer:

0.0065x + 1.25

Step-by-step explanation:

The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 138

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR  = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² -0.025x + 138

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

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If bert walks at 4 kilometers per hour and they meet in 5 hours, brends is walking at 1.5 km/h.

Since Bert and Brenda are walking towards each other, the distance between them will decrease at a combined rate of their walking speeds. Let's assume that Brenda's walking speed is x km/h.

We know that Bert walks at 4 km/h and they meet in 5 hours, so Bert has covered a distance of 4 × 5 = 20 km.

Let's use the formula distance = speed × time for Brenda. In 5 hours, Brenda would have covered a distance of 27.5 − 20 = 7.5 km.

So we have the equation:

7.5 = 5x

Solving for x, we get:

x = 1.5 km/h

Therefore, Brenda is walking at 1.5 km/h.

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Answer:

a =13

Step-by-step explanation:

180= (44+16-23)+11a

143=11a

143÷11= 13

Step-by-step explanation:

Total sales

Rs 5000- Rs 500= Rs 4500

The required amount received by the businessmen is 4500, from the sale.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the money businessman get be x,
According to the question,
x + commission of the agent = 5000

x + 500 = 5000
x = 4500

Thus, the required amount received by the businessmen is 4500.

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The inequality is solved to give the value of x as x≤ 4

Inequalities are defined as those expressions with unequal comparison of numbers, expressions, variables or even terms.

It is important to note the different signs of inequalities. They are;

From the information given, we have that;

9-7.25x ≤-20

Now, collect the like terms, we have;

-7. 25 ≤ - 20- 9

subtract the values given, we get;

-7.25x ≤ -29

Divide both sides by the coefficient of x, we get;

x ≤ - 29/7.25

Divide the values, we get;

x ≤ 4

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A multiple-choice quiz contains 5 questions. Each question has answer choices labeled a, b, c, and d. There are 256 different ways can a student answer the five questions.

Permutation and Combination:

Permutations and combinations form counting principles, which are applied in many different situations. A permutation is the number of different arrangements that can be made from a given set. When it comes to permutations, the details matter because the order or order matters. The three country names are spelled differently: {US, Brazil, Australia} or {Australia, US, Brazil) or {Brazil, Australia, US}, and the order in which the country names appear is important. In combination, the names of the three countries are just one group, and the order or sequence does not matter.

When asked how many ways an object can be combined, dispersed, mixed or split, in this case the answer is to use the counting method to calculate the number of ways.

In this case, DDDD can be answered from AAAA, AAAB, AAAC, AAAD, AABA, AABB, ..., CADB. To calculate that number, we have to consider that for every possible answer to one question, there are four alternatives to the other question. So for the 4 choices for question 1, there are 4 choices for question 2, and for each question 3, and so on.

Therefore, the answer is 4*4*4*4 = 256 questions.

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Answer:

1 1/4

Step-by-step explanation:

1/2 = 2/4

1 3/4 - 2/4 = 7/4 - 2/4 = 5/4 = 1 1/4

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In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.

The given cubic polynomial function is

f(x) = 4x³ + ax² + bx + k

f'(x) = 12x² + 2ax + b

f''(x) = 24x + 2a

At local maximum f' = 0

f'(0) = 12×(0)² + 2a×(0) + b = 0

b = 0

At local minimum, f' = 0

That is f'(-2) = 0 and f''(-2) > 0

f'(-2) = 12×(-2)² + 2a×(-2) + b = 0

48 - 4a + b = 0

4a - b = 48  

a = 12

Therefore, f(x) =  4x³ + 12x² + k

Integrate f(x)dx = 32 from 0 to 1, that is

∫₀¹ f(x)dx = 32

∫₀¹ (4x³ + 12x² + k) dx = 32

[ x⁴ + 4x³ + kx ]₀¹ = 32

(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32

1 + 4 + k = 32

k = 27

-- The question is incomplete, answering to the question below--

"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.

A. Find the values of a and b

B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"

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Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

here a₁ = - 1 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-5}{-1}\) = 5

then nth term is

\(a_{n}\) = - 1 \((5)^{n-1}\)

The Probability Density Function  (P.D.F) is : f(x) = {-2013e^(-2013x) for x ≥ 0, and 0 otherwise}.

The continuous random variable, X, has an inverse exponential distribution with parameter, λ

The probability density function (P.D.F) of a random variable is defined as the derivative of the cumulative distribution function (C.D.F) of the variable.

The cumulative distribution function is expressed as: P(X < x) = F(x)

Where F(x) is the C.D.F function of the random variable X.

In this case, since the random variable is an inverse exponential distribution, then the C.D.F is given by:F(x) = P(X ≤ x) = 1 - e^(-λx) where λ > 0 and x > 0.

This means that the P.D.F function, f(x) is given by the derivative of the C.D.F as follows:

f(x) = d/dx(F(x))

f(x) = d/dx(1 - e^(-λx))

          = λe^(-λx) where λ > 0 and x > 0

Therefore, the P.D.F is:f(x) = λe^(-λx) where λ > 0 and x > 0.

Assuming the inverse exponential distribution holds, find k such that:

f(x)={ ke−2013x  0x≥0

otherwise ​is a legitimate function.

We know that: f(x) = ke^(-2013x) for x ≥ 0 and 0 otherwise Also, we know that: ∫f(x)dx = 1, and f(x) ≥ 0 on the interval (0, ∞).

Therefore, we can integrate f(x) from 0 to ∞ as follows:∫(0, ∞) f(x) dx = ∫(0, ∞) ke^(-2013x) dx = k∫(0, ∞) e^(-2013x) dx => k[-e^(-2013x)/2013] from 0 to ∞

Using limits to evaluate k[-e^(-2013x)/2013] from 0 to ∞, we get:

lim x→∞ [-e^(-2013x)/2013] = 0, and [-e^(-2013(0))/2013] = -1/2013

Therefore, k[-e^(-2013x)/2013] from 0 to ∞ = k(-1/2013) = 1=>

k = -2013.

Hence, the P.D.F is:f(x) = {-2013e^(-2013x) for x ≥ 0, and 0 otherwise}.

This is a legitimate P.D.F function since f(x) > 0 for all x > 0, and ∫f(x)dx = 1.

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Answer:

Step-by-step explanation:

The function with a constant additive rate of change of –1/4 is a straight line with a negative slope. The line passes through the points (negative 2, 2) and (2, 1), which means that for every four units that x increases, the corresponding y value decreases by one unit. This can be represented by the equation

y = (-1/4)x + 3/2.

A curved line passing through (negative 1, 2), (0, negative 1), the minimum

(2, negative 2), and

(4, 1) does not have a constant additive rate of change and cannot be the function in question.

Answer:

D. The opposite sides are congruent

Answer:

f(x) = 9(x + 5)2 - 6 (-5,-6)

f(x) = 6(x + 9)2 - 5 (-9,-5)

f(x) = 9(x - 5)2 + 6 (5,6)

f(x) = 6(x - 5)2 - 9. (5,-9)

f(x) = 5(x - 6) +9. (6,9)

Step-by-step explanation:

To find the vertex: for the x-coordinate, take the "h" in the parentheses (x + h) and reverse its sign. For the y-coordinate, use the "k" term as-is.

The coordinates of the vertex of the equations are:

The vertex form of the quadratic function is given as:

y = a(x -h)^2 + k

Where:

Vertex = (h,k)

Using the above highlight, the coordinates of the vertex of the equations would be:

f(x) = 9(x + 5)^2 - 6

Vertex = (-5,-6)

f(x) = 6(x + 9)^2 - 5

Vertex = (-9,-5)

f(x) = 9(x - 5)2 + 6

Vertex =(5,6)

f(x) = 6(x - 5)^2 - 9

Vertex = (5,-9)

f(x) = 5(x - 6) +9

Vertex = (6,9)

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Answer:

a. K3080

Step-by-step explanation:

K2000×10/100=K200

K80×36months=2880

K2880+K200=K3080