Which length in cm should be recorded for the red line in the figure above

Ted's net pay per week after the taxes is $559.09

Net Pay:

Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.

Given,

Ted works as a travel guide for a mountain resort, earning $15.72 per hour. Ted is paid weekly, and works 40 hours in one week. His current federal withholding per week is $69. He works in a state with a flat-rate income tax of 4.63%. He will receive a raise of 5% of his hourly rate.

Here we need to find the Ted's net pay per paycheck, after taxes, if his new federal withholding per week is $75.

Through the given details we know that,

Per hour pay = $15.72

Total work per week = 40

So, the total amount for a week is

=> 15.72 x 40

=> $628.8

After federal withholding tax, then the amount is

=> $628.8 - 69

=> $559.8

Now the tax is 4.63%, then

=> $559.8 x 4.63%

=> $559.8 x (4.63/100)

=> $25.91

So, the remaining amount is

=> $559.8 - $25.91

=> $533.88

Now, he will receive 5% for his hourly rate,

Then,

=> $15.72 x (5%)

=> $15.72 x (5/100)

=> 0.78

So, the increased amount is

=> $16.5

Now, the net pay is,

=> (16.5 * 40) - (75 + 25.91)

=> 660 - 100.91

=> 599.09

So, Ted's net pay per paycheck, after taxes is $559.09.

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The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89

Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).

The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).

Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.

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Answer:

6

Step-by-step explanation:

Using the equation of the parabola, the inequality represented is:

y ≥ -(x + 2)² + 8.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (-2,8), hence:

h = -2, k = 8.

y = a(x + 2)² + 8.

The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:

4 = 4a + 8

4a = -4

a = -1.

Hence the parabola is:

y = -(x + 2)² + 8.

The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:

y ≥ -(x + 2)² + 8.

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Answer:

D. 24

Step-by-step explanation:

The area of a triangle is [tex]\frac{1}{2} (bh)[/tex].

The height is already given: 8

But we need to find the base and since the hypotenuse is given and it's a right triangle, we can use the pythagorean theorem. (Hypotenuse is longest, slanted side of a right triangle)

The pythagoren theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the sides, and c is the hypotenuse.

Plugging in the given values => [tex]8^2+b^2=10^2[/tex]

We have to solve for b. So, squaring 8 and 10 we get [tex]64+b^2=100[/tex].

Next, subtract 64 from both sides to get b by itself: [tex]b^2=36[/tex]

Square root both sides to get [tex]b=6[/tex].

Now that we have our base we can plug it in to the area of triangle formula: [tex]1/2(6*8)[/tex].

Multiply inside the parenthesis: 1/2(48) => 24

Answer:

14

Step-by-step explanation:

44.66 / (12.76 / 4) = 14

The solution to the system of linear equations shows that the cost of 1 kg of turnips is £ 1.1 and the cost of 1kg of mushrooms is  £ 2.9.

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

First, you should convert the text of the problem into equations, thus you can write:

2m + 2.5t = 8.55 (1)

3m + 4t = 13.10  (2)

where: m = mushrooms and t = turnips

For solving this question, you can apply the addition method. Thus, you should follow the steps below:

           6m + 7.5t = 25.65 (1)

          -6m -8t = -26.20  (2)

         -0.5t = -0.55

          0.5t = 0.55

From equation 1, you have 6m+7.5t=25.65 . If t= 11/10, you have

6m + 7.5*11/10 = 25.65 * (100)

600 m + 825 = 2565

600 m = 2565 -825

600 m = 1740

m = 1740/600

m=29/10

m=2.9

From the previous steps, you have the answers for the letter a ( £ 2.9 ) and the letter b ( £ 1.1).

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The equation is 7x+11y+14z=33.

So,

The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:

It is assumed that the required plane's x-intercept is twice its z-intercept.

Substitute k = 4/5 in equation (1) as follows:

As a result, the required plane's equation is 7x+11y+14z=15.

Also,

7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.

Therefore, the equation is 7x+11y+14z=33.

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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.

Answer: 43.6 cm

Step-by-step explanation:

18.6+3.2= 21.8

21.8*2= 43.6

Answer:
True for all x/infinite solutions.

Step-by-step explanation:

[tex]4x+6=2\left(2x+3\right) < - Base Equation[/tex][tex]4x+6=4x+6 < - Expand-The-Equation-and-Simplify![/tex]
[tex]4x+6-6=4x+6-6 < - Subtract-Six-From-Both-Sides![/tex]
[tex]4x=4x[/tex]
[tex]4x-4x=4x-4x < - Subtract -4x- from- both -sides![/tex]
[tex]0=0[/tex]
________________________________________________________
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Answer:

30

Step-by-step explanation:

30*30 is 900

Answer:

30

Step-by-step explanation:

let x =width

900=(×)(30)

900=30×

900/30=30×/30

30=×

= 30 width

The correct number that represents the output of the print statement is 31

The program segment is given as

for numX in [3]

   for numy in [1]

       print (numX, numy)

The program flow of the above program segment is:

In the above iterations, we have the following values

numX = 3

numY = 1

When both values are printed, we have the output to be 31

Hence, the correct number that represents the output of the print statement is 31

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Answer:

answer 1 = 3,5

answer 2 = 1,4

Step-by-step explanation:

The location of the midpoint of the line segment is (37 / 2, 11 / 2).

According to the statement, the position of the two endpoints of a line segment are known and we must determine where the midpoint is, that is, the point such that the line segment is divided into two parts of equal length. The location of the midpoint is found by means of the midpoint formula:

M(x, y) = 0.5 · B(x, y) + C(x, y)        

Where M(x, y) is the midpoint.

If we know that B(x, y) = (15, 7) and C(x, y) = (22, 4), then the location of the midpoint is:

M(x, y) = 0.5 · (15, 7) + 0.5 · (22, 4)

M(x, y) = (15 / 2, 7 / 2) + (11, 2)

M(x, y) = (37 / 2, 11 / 2)

The location of the midpoint of the line segment is (37 / 2, 11 / 2).

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The value of the linear equation after adding is -5x -8y = -5.

According to the statement

We have to find that the value of the linear equation.

So, For this purpose, we know that the

The linear equation, statement that a first-degree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant.

From the given information:

The given equations are:

4x-4y = -2

-9x-4y = -3.

Then

Now, add these equations then

4x-4y = -2 + -9x-4y = -3.

4x-9x-4y-4y = -2-3

-5x -8y = -5

After addition ,the value becomes -5x -8y = -5.

So, The value of the linear equation after adding is -5x -8y = -5.

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Answer:

Equation: P=$2500+$120N

Total pay if  Miguel sells 23 copies: $5260

A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except dependent.

Any variable employed in research that has a cause and effect relationship is referred to as a research variable (also known as a study variable) informally. An array of variables, including independent factors, dependent variables, and intervening variables, can be employed in a study, including research/study variables.

Independent and dependent variables are crucial in research since they provide the framework for a study to be carried out. Confounding factors, controlled variables, superfluous variables, and moderator variables are some other sorts of variables that could be used in a research.

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Inference is referred to as all the data collected in a particular study.

Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.

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Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).

Roots of an equation refer to the values that when put into the variable of the equation, satisfy the equation and give the required value as 0.

Given:

g(x) = 3x⁵ - 2x⁴ + 9x³ - x² + 12 = 0

To find: Function having same set of potential rational roots as g(x).

Finding:

=> Then, m = ±1, ±2, ±3, ±4, ±6

    2. Let 'n'  denote the rational roots of 3.

=> Then n = ±1, ±3

Hence, the rational roots [tex]\frac{m}{n}[/tex] will be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].

The rational roots will be taken of 12 and 3 in the same position as in g(x).

Hence, the rational roots of f(x) will also be given by:   ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].

Thus, Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).

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(COMPLETE QUESTION:

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?

A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12

B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x

C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3

D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48)

The system of equations involving y = 2x and y = -x + 6 has the solution (2 , 4).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

y = 2x     (equation 1)

y = -x + 6     (equation 2)

Since both equations are in the form of y in terms of x ans dome constant, substitute the first equation to the second equation.

y = -x + 6     (equation 2)

2x = -x + 6

Combining the all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.

2x + x = 6

3x = 6

x = 2

Substituting the value of x in the first equation,

y = 2x     (equation 1)

y = 2(2)

y = 4

Writing it as an ordered pair, we got (2 , 4) as the solution of the system of equations involving y = 2x and y = -x + 6.

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Answer:

Rotation

Step-by-step explanation:

Rotation at the origin (0,0) by 180*

Answer:

One motorcycle was going 44 miles and hour and the other motorcycle was going 8 miles an hour faster, so it was going 52 miles per hour.

Step-by-step explanation:

Distance = rate times time

Both motorcycles have a time of 3.  We do not know the rates, but we know that one motorcycle's rate was 8 miles an hour faster.  Let's call motorcycle 1's rate x then motorcycle 2's rate must be (x + 3)

Motorcycle 1

d = 3x

Motorcycle 2

d = 3(x +8)

We know that the total distance together is 288

3x + 3(x+8) = 288  Distribute the 3

3x + 3x + 24 = 288  Combine the 3's

6x + 24 = 288  Subtract 24 from both sides of the equation

6x = 264  Divide both sides by 6

x = 44

One motorcycle was going 44 miles and hour and the other motorcycle was going 8 miles an hour faster, so it was going 52 miles per hour.

Answer:-4.6

Step-by-step explanation:

Answer: I calculated the surface area of a cube whose edge is 4.2 m

Step-by-step explanation: hope this helps

The ball will fall 35d after 5t seconds.

Equation Of Motion is used to define the basic concept of motion of object at various interval of times.

There are three equation of motion

[tex](i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as[/tex]  (where s=distance, v=final velocity, u=initial velocity ,t=time,          a=acceleration)

According to the given question

Given distance = d

time=t

Acceleration a=g( gravity)

Using second equation of motion

[tex]d=ut+\frac{1}{2} at^{2}[/tex]     ( given u=0 as the ball was at rest, a=g , s=d)

[tex]d=\frac{1}{2} gt^{2}[/tex]........(1)

Using first equation of motion

Speed after t sec

[tex]v=u+at\\ \\ v=0+gt\\ \\ v=gt[/tex]    ....... (2)

Using second equation of motion distance after 5t seconds

since ball is moving with velocity "v", t=5t.

[tex]s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}[/tex]

Substituting the value v=gt from equation (2)

[tex]d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}[/tex]taking LCM as 2 and solving further we get

[tex]=35(\frac{1}{2}gt^{2} )[/tex]    

using equation (1) we get

=35d

Therefore , The ball will fall 35d after 5t seconds.

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The circumference of track 3 is 691.43 feet

The circumference of a circle is the distance round the circle. It is the perimeter of the circle. The radius of a circle is a straight line that goes from the center of the circle to its circumference.

The circumference of a circle = 2πr

Where:

2 x (22/7) x 110 = 691.43 feet

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Answer:

7/6

Step-by-step explanation:

Answer:

48.25 minutes

Step-by-step explanation:

Divide 1544/32 to find the time per student

Answer:

d = 2

YZ = 16

Step-by-step explanation:

X-Y-Z

so XY + YZ = XZ

11d + (9d -2) = 5d + 28

11d + 9d - 5d = 28 + 2

15d = 30

d = 30/15 = 2

YZ = 9d - 2 = 9(2) - 2 = 18 - 2 = 16