an electrician charges a flat service fee to accept a job and an additional hourly rate to complete the job. the amount an electrician charges per job can be represented by the function e(x)

The value of k to the nearest integer is 21

If the number of international tourist arrivals in Russia in 2012 was 13.5% greater than in 2011 will be expressed as:

k = 24.7 - (13% of 24.7)

k = 24.7 - (0.135 * 24.7)

k = 24.7 - 3.3345

k = 21.3655

Hence the value of k to the nearest integer is 21

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In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n          

                                                                                                                        In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n            

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n                                                                                                                                                                        we need to perform the inverse Z-transform. The inverse Z-transform converts a function in the Z-domain back into the time domain.

The general form of the inverse Z-transform is given by:

f(n)= \(\frac{1}{2\pi j}\) ∮ \(_{C}\) \(F(z)z^{n-1} dz\)

​ where

F(z) is the function in the Z-domain, f(n) is the corresponding time-domain sequence, j is the imaginary unit, and ∮\(_{c}\)

​represents integration around a closed path in the Z-plane.

In this case, the function F(z) is a rational function, and we can find its inverse Z -transform using partial fraction decomposition. Let's find the inverse Z-transform step by step:

Step 1: Express F(z) in partial fraction form.

\(F(z)=\frac{1}{z^2} + \frac{3}{z} +4\)

Step 2: Find the roots of the denominator The roots of \(z^{2} =0\) and

z=0 (a double pole at the origin).

Step 3: Perform partial fraction decomposition.

We can write \(F(z)=\frac{A}{z} +\frac{B}{z^2} ​\)

​Multiplying through by \(z^{2}\) to clear the fractions we get,\(1+3z^{-1} +4z^{-2} = A+Bz^{-1}\)                                                                                                        Comparing coefficients, we get:

A=1

B=4

Step4: Apply the inverse Z transform for each term

Inverse Z transform for A/z is \(a^{n}\), where a is the root of corresponding term in the denominator. In this case a=0, so the inverse Z transform of A/z=1

The inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\), where a is the root of the corresponding term in denominator. In this case a=0. So the inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\)=0

therefore the time domain of function f(z) is

f(n)=1+0=1

So the sampled time domain representation of the function F(z)=\(1+3z^{-1} +4z^{-2}\) is f(n)=1 for all the values of n

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Answer:

WHAT

Step-by-step explanation:

Answer: 7\(\sqrt{2}\)

Step-by-step explanation: Khan Academy

Answer:

8 nine tenths

Step-by-step explanation:

Answer:

The slope is: \(\frac{3}{4}\)

Step-by-step explanation:

The equation for slope is:

\(m=\frac{y_{2}- y_{1} }{x_{2} -x_{1} }\)

Point 1: -3=\(x_{1}\), -2=\(y_{1}\)

Point 2: 5=\(x_{2}\), 4=\(y_{2}\)

4-(-2)=6

5- (-3)=8

6/8=3/4

Answer:

4%

Step-by-step explanation:

Yearly salary = 9600 * 12 = Rs. 115200

Tax = Rs . 4530

\(Tax \ percent = \frac{4530}{115200}*100\)

                    = 3.93 = 4%

The valid sampling method(s) for obtaining a sample of individuals with high cholesterol from the list provided are simple random sampling, stratified sampling, and cluster sampling.

- Simple random sampling: This method involves randomly selecting 40 individuals from the list of 6800 individuals.

- Stratified sampling: This method involves dividing the list of 6800 individuals into different strata  based on relevant characteristics.

- Cluster sampling: This method involves dividing the list of 6800 individuals into smaller clusters (e.g., primary care physician offices or geographical areas).

This method is useful when it is difficult or costly to reach individuals scattered across a wide area.

Each of these methods has its advantages and disadvantages, so the choice depends on the specific needs and constraints of the pharmaceutical company.

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Answer:

-232

Step-by-step explanation:

9+12=21

21-219= -198

-198-22= -232

Answer:

10.6m

Step-by-step explanation:

height of cylinder:

h= V/pie r^2

h= 48/3.14x1.2^2

h=48/3.14x1.44

h=48/4.5216

h=10.61meter

round to the nearest tenth

= 10.6m

Please mark as brainliest

Answer:

it will be (3)

Step-by-step explanation:

since DB is a median

then DB= half AC , AB=BC

then AB=BD

then the two triangles are isosceles

The required m∠BDC is 32° .

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

According to the given question ;

DB is a median;

By the symmetry ;

Then DB = half AC ,

        = AB = BC

Then= AB = BD

In a triangle, a line that connects one corner (or vertices ) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle congruence, is that in an isosceles triangle the median to the base is perpendicular to the base.

Then the two triangles are isosceles.

Means m∠DAB = m∠BDC = 32°

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Answer:

6

Step-by-step explanation:

5^2+6=31

25+6=31

31=31

proved

One-third of the number is at least 5 units from 31. The number is 78.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that one-third of a number is at least 5 units from 31. The unknown number is x.

( 1 / 3 )x + 5 = 31

x + 15 = 31 x 3

x + 15 = 93

x = 93 - 15

x = 78

Therefore, one-third of the number is at least 5 units from 31. The number is 78.

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Answer:

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article. There are three main forms of linear equations.

Step-by-step explanation:

Answer:

I belive it is the second one

Step-by-step explanation:

Answer:

B. The second box plot

Step-by-step explanation:

Answer: 21.45$

Step-by-step explanation: I can’t explain how i got it but i hope this helped!

Answer:

$43.55

Step-by-step explanation:

I took 65 and found 33% by making 33% .33 and did 65*33, then subtracted what I got from the total of 65, 65-21.45 which is $43.55.

Answer:

72π feet

Step-by-step explanation:

circumference of circle= 2πr

Diameter= 2(radius)

radius of circle

= 72 ÷2

= 36 ft

Circumference

= 2(π)(36)

= 72π ft

Answer:

(x-4)²+4

Step-by-step explanation:

Answer:

\((x-4)^2+4\)

Step-by-step explanation:

\(x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4\)

To prove the equation \(\frac{1}{\tan(2\theta) - \tan(\theta)} - \frac{1}{\cot(2\theta) - \cot(\theta)} = \cot(\theta)\) we'll simplify the left side, this is shown below:

Using the trigonometric identities \(\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}\) and \(\cot(\theta) = \frac{1}{\tan(\theta)}\)

We can rewrite the expression as \(\frac{1}{\tan(\theta)(1 - \tan(\theta))} - \frac{\tan(\theta)}{\tan(\theta)(1 - \tan^2(\theta))}\)

Combining the fractions with a common denominator, we obtain \(\frac{1 - \tan(\theta)}{\tan(\theta)(1 - \tan(\theta))}\)

Simplifying further, we cancel out the \((1 - tan(\theta))\) terms, leaving us with \(\frac{1}{\tan(\theta)}\) = \(\cot(\theta)\), which is equivalent to the right side of the equation.

Thus, the equation is proven.

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On dividing the whole equation by

$a_{n+2}$

and taking the limit as

$n \rightarrow \infty$,

we get:

$$\lim_{n\to\infty} \frac{(n+2)(n+1)a_{n}}{a_{n+2}} = 2$$

This is the ratio test to determine the radius of convergence of the power series. Since the limit is 2, the radius of convergence is 1/2. Therefore, the minimum radius of convergence of power series solutions about the ordinary point xo = 2 is 1/2.

The differential equation can be expressed as

:$(x^3 - 2x^2 + 3x)y"+ x(x-3)^2 y' - (x + 1)y

= 0$

The first step to find the power series solution of the differential equation is to verify that

xo

= 2

is a point of the ordinary differential equation. Since both coefficients in this case are analytic at x

= 2, 2 is an ordinary point.Let

$y

= \sum_{n=0}^{\infty} a_n(x-2)^n$

be the power series solution of the given differential equation. Then

,$y'

= \sum_

{n=1}^{\infty} a_nn(x-2)^{n-1}$and $y''

= \sum_{n

=2}^{\infty} a_nn(n-1)(x-2)^{n-2}$

Substituting these in the differential equation we get

:$(x^3 - 2x^2 + 3x)\sum_{n

=2}^{\infty} a_nn(n-1)(x-2)^{n-2}+ x(x-3)^2 \

sum_{n=1}^{\infty} a_nn(x-2)^{n-1} - (x + 1) \sum_{n=0}^{\infty} a_n(x-2)^n

= 0$$$\sum_{n=0}^{\infty} [a_{n+2}(n+2)(n+1)x^{n+1} -2a_{n+1}(n+2)x^{n+1} + 3a_n x^{n+1}] + \

sum_{n=1}^{\infty} [a_n x^{n+2} - 3a_n x^{n+1} + 2a_n x^n] - \sum_{n=0}^{\infty} [a_n x^{n+1} + a_n x^n]

= 0$$

Comparing the coefficients of

x^n, we have:

$a_{n+2}(n+2)(n+1) - 2a_{n+1}(n+2) + (3-a_n)

= 0$

On dividing the whole equation by

$a_{n+2}$

and taking the limit as

$n \rightarrow \infty$, we get

:$$\lim_{n\to\infty} \frac{(n+2)(n+1)a_{n}}{a_{n+2}}

= 2$$

This is the ratio test to determine the radius of convergence of the power series. Since the limit is 2, the radius of convergence is 1/2. Therefore, the minimum radius of convergence of power series solutions about the ordinary point xo

= 2 is 1/2.

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The acute angle that the ladder makes with the ground is 70.94°.

To work out the size of the acute angle that the ladder makes with the ground, we need to use trigonometry. Let's call the angle we're trying to find "theta" (θ). We know that the ladder is the hypotenuse of a right-angled triangle, with the wall being one side and the ground being the other. Using the Pythagorean theorem, we can work out the length of the ladder's side of the triangle:
a² + b² = c²
where a = 1.8m (the distance from the wall to the base of the ladder), b =? (the distance from the base of the ladder to the ground), and c = 5.1m (the length of the ladder).
Rearranging this formula, we get:
b² = c² - a²
b² = (5.1)² - (1.8)²
b² = 24.21
b = √24.21
b = 4.92m (to 2 decimal places)
Now that we know the lengths of the sides of the triangle, we can use trigonometry to find the angle θ. Specifically, we can use the tangent function:
tan(θ) = opposite/adjacent
where opposite = b (the distance from the base of the ladder to the ground) and adjacent = a (the distance from the wall to the base of the ladder).
tan(θ) = 4.92/1.8
tan(θ) = 2.7333 (to 4 decimal places)
Now we need to find the inverse tangent (or arctan) of this value to get the angle θ:
θ = arctan(2.7333)
θ = 70.94° (to 1 decimal place)
Therefore, the acute angle that the ladder makes with the ground is 70.94°.

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Answer:

B: 375 ft^2

Step-by-step explanation:

20 x 15 + 10 x 15/2 = 375

Any p-value less than 0.05 is a cause to reject the null hypothesis.

What is Null Hypothesis?

The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.

In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).

Any p-value less than 0.05 is a cause to reject the null hypothesis.

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Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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Answer:

Step-by-step explanation:

B

The solution to the given set of equations is Infinite solutions.

We have the equation

R: -3y = -3x -9

S: y = x + 3

Now, solving the equation R and S as

-3y = -3x - 9

3y =  3x + 9

_________

   0 = 0 + 0

   0 = 0

Also, -3/1 = 3/(-1) = 9/(-3)

-3/1 = -3/1 = -3/1

Thus, the equation have Infinite many solutions.

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The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented  as - 96a + 84b + 32x + 24y

Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

Therefore, the equivalent expression of  −12(8a − 7b) + 8(4x + 3y) can be solved as follows:

−12(8a − 7b) + 8(4x + 3y)

open the bracket

−12(8a − 7b) + 8(4x + 3y)

- 96a + 84b + 32x + 24y

Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y

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122° and angle 1 are alternate interior angles and hence they are equal.

m1 = 122°

122° + angle 2 = 180° [sum of co interior angles is 180°]

angle 2 = 180° - 122°

m2 = 58°

Answer:

A

Step-by-step explanation:

Using the standard form of the parabola , y = ax² + bx + c ( a ≠ 0 )

Substitute the given points into the equation and solve for a, b, c using simultaneous equations.

(- 5, 10 )

- 10 = a(- 5)² - 5b + c, that is

25a - 5b + c = - 10 → (1)

(- 3, 2 )

2 = a(- 3)² - 3b + c, that is

9a - 3b + c = 2 → (2)

(2, - 3 )

- 3 = a(2)² + 2b + c , that is

4a + 2b + c = - 3 → (3)

Eliminate c from the equations

Subtract (2) from (1) term by term

16a - 2b = - 12 → (4)

Subtract (3) from (2) term by term

5a - 5b = 5 → (5)

Multiply (4) by 5 and (5) by - 2 then add to eliminate b

80a - 10b = - 60 → (6)

- 10a + 10b = - 10 → (7)

Add (6) and (7) term by term

70a = - 70 ( divide both sides by 70 )

a = - 1

Substitute a = - 1 into (4) and evaluate for b

- 16 - 2b = - 12 ( add 16 to both sides )

- 2b = 4 ( divide both sides by - 2 )

b = - 2

Substitute a = - 1, b = - 2 into (3) and evaluate for c

- 4 - 4 + c = - 3

- 8 + c = - 3 ( add 8 to both sides )

c = 5

Thus a = - 1, b = - 2 and c = 5

Substitute these values into the standard parabola, that is

y = - x² - 2x + 5 → A

Here we want to find the equation of the parabola that passes through the points (-5, -10), (-3, 2), and (2, -3).

We will get, by brute force, that the correct option is A:

y = -x^2 - 2x + 5

To find the correct option we can use brute force.

We do know the options, so what we can do is just evaluate the given options in the x-values of the points, and see if we get the same y-value that the point.

We can start with option A:

A: y = -x^2 - 2x + 5

For the first point (-5, -10) we have x = -5, evaluating in this we get:

y = -(-5)^2 - 2*(-5) + 5 = -25 + 10 + 5 = -10

Now let's try with the next point (-3, 2), we have x = -3

y = -(-3)^2 - 2*(-3) + 5 = -9 + 6 + 5 = 2

Now we can try with the last point (2, -3), where x= 2

y = -(2)^2 - 2*2 + 5 = -4 - 4 + 5 = -3

So we got all the correct y-values (the second value for each point) thus we can conclude that this one is the correct option.

The correct option is A: y = -x^2 - 2x + 5

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Answer:

18 / 19

Step-by-step explanation:

Divide it by 2

Answer:

You subtracted 25 from both sides.

Step-by-step explanation:

To move one part of the equation to the other side, you need to do the opposite. 25 is already negative(or being subtracted) so you need to add it to both sides to cancel it out on the left.

10x=-75+25

10x=-50

then divide both sides by 10

x=-5