if a ray of light strikes mirror 1 with an angle of incidence of 41 ∘ , find the angle of reflection of the ray when it leaves mirror 2.

The area of the paperboard that remains is 268.83 square inches.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, a rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out.

Area of rectangular paperboard length×width

= 22×18

= 396 square inches

Area of a semicircle = 1/2 ×πr²

Here, r=18/2 = 9 inches

= 1/2 ×3.14×9²

= 127.17 square inches

So, remaining area = 396-127.17

= 268.83 square inches

Therefore, the area of the paperboard that remains is 268.83 square inches.

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Assuming the underlying system is casual with zero initial conditions, the transfer function is Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z).

The differential equation is y(n) = 3y(n-1) + x(n − 2).

Since there are no initial conditions, the underlying system is known to be casual.

Considering the Transfer function.

Z transform properties are used

y(n-1) = [tex]z^{-1}[/tex]Y(z)

y(n) = Y(z)

x(n-2) = [tex]z^{-2}[/tex]X(n)

Now putting the value in the equation

Y(z) = 3[tex]z^{-1}[/tex]Y(z) + [tex]z^{-2}[/tex]X(n)

Multiply by [tex]z^2[/tex] on both side, we get

[tex]z^2[/tex]Y(z) = 3zY(z) + X(n)

Subtract Y(z) 0n both side, we get

[tex]z^2[/tex]Y(z) - 3zY(z) = X(n)

Y(z)([tex]z^2[/tex] - 3z) = X(n)

Divide by ([tex]z^2[/tex] - 3z) on both side, we get

Y(z) = X(n)/([tex]z^2[/tex] - 3z)

Divide by X(n) on both side, we get

Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z)

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The equations are solved to give

1. y = 13

2. x = 3

3. b = 3

It is important to note that algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.

From the information given, we have that the expressions are;

3y+5=2y-8

Now, collect like terms

3y - 2y = -8 - 5

subtract the like terms

y = 13

-2(x-1)=3x-13

expand the bracket

-2x + 2= 3x - 13

collect like terms

-2x -3x = -13 - 2

subtract the like terms

-5x = -15

x = 3

3b+4+b=16

collect like terms

4b = 12

b = 3

Hence, the values are 13. 3 and 3

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The length of the picture is 30 meters

From the question, we have the following parameters that can be used in our computation:

Area = lb

Also, we have

Area = 3 * 125

Where

Width = 1.25 meters

Substitute the known values in the above equation, so, we have the following representation

3 * 125 = Length * 1.25

Divide both sides by 1.25

Length = 30

Hence, the length is 30 meters

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Answer:gdp

Step-by-step explanation:gross domestic product

Answer:

GDP => Gross Domestic Product

Step-by-step explanation:

GDP measures the monetary value of final goods and services produced in a country in a given period of time

Answer:

0.26

Step-by-step explanation:

There are 1 + 3 + 2 + 10 + 9 + 7 + 3 = 35 total students. Additionally, there are 9 students who work exactly 4 hours. Thus, the probability is 9/35, or 0.26 rounded to the nearest hundredth.

Answer:

26

Step-by-step explanation:

1+3+2+10+9+7+3= 35

35 divided by 4

A team's winning percentage is calculated as follows:

D. PCT = games won/total games played.

A team's winning percentage is obtained applying a proportion, as the percentage is given by the division of the number of desired outcomes, that is, the number of games won, by the total number of outcomes, that is, the number of games played.

Hence the equation used to calculate the percentage is given as follows:

PCT = games won/total games played.

Meaning that the correct option is given by option D.

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Answer:

Step-by-step explanation:

620 cm^2

Step-by-step explanation:

Area of isosceles triangles:

A = (b×h) ÷ 2

Substitute

(24 × 5) ÷ 2

120 ÷ 2 = 60 cm^2

There are 2 triangles so:

60 × 2 = 120 cm^2

Area of 2 identical rectangles:

- They are identical and this is shown by the two short lines which indicate that this is an isosceles triangle. They have 2 identical sides.

A = L × W

Substitute

10 × 13 = 130

Because there are two:

130 × 2 = 260 cm^2

Area of the rectangle at the bottom:

- Let's not forget the rectangle at the bottom of this shape.

A = L × W

Substitute

24 × 10 = 240 cm^2

Add these all together to get the total surface area:

120 + 260 + 240 = 620 cm^2

Answer: 620 cm^2

Answer:

620cm squared

Step-by-step explanation:

a=bxh/2

so this means

24x5/2=area of one triangle(60cm squared)

since there are two .that means the area for both triangles is 120cm squared

for the recatngles:

a=lxw

Substitute

10 × 13 = 130

since there are 2 of them,

130 × 2 = 260 cm^2

the rectangle on the bottom:

a=lxw

24x10=240cm squared

240+260+120=620

The nurse should run the pump at 111.1 ml/hr.

To infuse a 1000ml bag of lactated ringers over 9 hours, the nurse must determine the hourly rate at which the fluid should be infused. This can be done by dividing the total volume of the fluid (1000 ml) by the number of hours it will take to infuse it (9 hours).

So, the hourly rate would be:

1000 ml ÷ 9 hours = 111.1 ml/hr.

Therefore, the nurse should run the pump at 111.1 ml/hr in order to infuse the 1000ml bag of lactated ringers over 9 hours.

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By applying linear equation concept, it can be concluded that the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.

Linear equation is an equation that contains one or more variables, where each variable has the power of one.

Linear equation graph with a particular slope will be formed if this equation is depicted in a Cartesian diagram. The slope is usually called the gradient of the line (m), so the equation can be written as y = mx + c.

If the line graph is sloping to the right indicates that the gradient is positive. Conversely, if the line graph is sloping to the left indicates that the gradient is negative.

Therefore, the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.

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Step-by-step explanation:

the simplest way for me is

1. to convert both terms into full fractions (not mixed numbers).

2. then to bring both fractions to the same denominator.

3. and then do the actual calculation.

and if needed, we can

4. then convert the result back into mixed numbers.

1.

15 1/2 = (15×2 + 1)/2 = 31/2

1 11/20 = (1×20 + 11)/20 = 31/20

2.

we need to convert 31/2 into a fraction .../20, so that we can actually combine it with the 31/20.

how do we get from 2 to 20 ? by multiplying by 10.

in order to keep the value of the fraction unchanged, we need to do the same multiplication also to the numerator :

31/2 × 10/10 = 310/20

3.

310/20 + 31/20 = 341/20

4.

341/20 = (17×20 + 1)/20 = 17 1/20

to get this you do an integer division and note the remainder.

341/20 = 17 remainder 1

Answer: angle dce is the angle that is vertical

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

Here i attached answer.

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The order of the group generated by matrices a and b under matrix multiplication is a process of multiplying the matrices and counting the number of distinct matrices that can be produced.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The order of a group generated by matrices a and b refers to the number of distinct matrices that can be produced by multiplying a and b a certain number of times.

To find the order of the group, we need to start by multiplying a and b and see if we get any new matrices. If we do, we keep multiplying those matrices until we get back to the original matrices a and b.

The order of the group is the number of distinct matrices we get in this process.

It is important to note that matrix multiplication is associative, which means that the order in which we multiply the matrices does not affect the result. Also, the identity matrix is a special matrix that, when multiplied by any matrix, produces the same matrix.

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The required value of w in the given expression is 1, as per the given conditions.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The question seems to be incomplete, assume that the given expression 8w + 5 = 13
So

8w + 5 = 13
simplify

8w = 13 - 5
w = 8 / 8
w = 1

Thus, the required value of w in the given expression is 1, as per the given conditions.

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For the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.

The space enclosed by a pentagon's sides is referred to as the pentagon's area. Various techniques can be used to compute it depending on the dimensions that are known. The kind of pentagon also makes a difference. For instance, if it is a normal pentagon, the area can be determined using a single formula; but, if it is an irregular pentagon, we must divide it into various polygons and add their areas to determine the pentagon's area.

The perimeter is the sum of length of all the sides of a pentagon.

P = 5s

P = 5(7.4) = 37 units.

The area of the pentagon is given as:

A = 1/2 (P)(a)

Substitute the value of P = 37 and a = 6.4086:

A = 1/2 (37)(6.4086) = 118.55 square units.

Type: Pentagon.

Hence, for the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.

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The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

m2 = 210 kg

Using the equation for a hydraulic lift, the force on each mass can be calculated.

F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

210 kg = m2 x 9.8 m/s2

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

Plug in the given values:

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

Solve for m2:

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

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The function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )

%y = nthTaylorPolyExp( n, x )is a function that returns 3rd Taylor polynomial of exponential function at x=0.

%       n is an input argument, which indicates the degree of Taylor

%           polynomial.

%       x is an input argument

%       y is the output.

y=zeros('like',x);

% ============= YOUR CODE HERE ==============

% Instructions: Return nth Taylor polynomial of exponential function at x=0.

%               You can use built-in function factorial(n) to return n!,

%               and use for loop to get the sum.

for i = 0:n

     % y = y + (-1)^i * (x.^(2 * i)) / factorial(2 * i); is my version, but its incorrect.

end

Thus, the function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )

Complete question: How do I write the function to derive an nth taylor polynomial?

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Answer:

see bleow

Step-by-step explanation:

supplementary simply means angle 1+ which angle =180

so angle 2 & 4 are supplementary.

if angle 1 = 124, then angle 4 = angle 2 = 180-124 =56

angle 3 = angle 1 =124

The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is [tex]y = 7x - 6/7 + 1.[/tex]

[tex]y' = (7e7x + 7x - 1)/7xy[/tex]

1. Use implicit differentiation to differentiate both sides of the equation with respect to x:

[tex]ln 7xy = e7x − y ln 7xy + (7xy) (y') = (7e7x) + (e7x)(7)[/tex]

2. Solve for y':

[tex]y' = (7e7x + 7x - 1)/7xy[/tex]

3. Plug in the given point to find the slope at that point:

[tex]y' = (7e(1/7) + (1/7) - 1)/(7*(1/7)*1) = (7 + 1 - 1)/1 = 7[/tex]

4. Use the point-slope form of a line to find the equation of the tangent line:

[tex]y - 1 = 7(x - 1/7)y = 7x - 6/7 + 1[/tex]

The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is[tex]y = 7x - 6/7 + 1.[/tex]

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Histogram is a visual representation of data distribution and a stem and leaf plot provide individual values in a set.

Pros of a histogram:

Cons of a histogram:

Pros of a stem-and-leaf plot:

Cons of a stem-and-leaf plot:

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As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)

The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.

We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).

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Complete question -

the capture rate will be lower than what is indicated in the confidence level.

A C% confidence interval gives an interval of plausible values for a parameter. The interval is calculated from the data and has the form, point estimate ± margin of error.

When the random and large counts conditions are met, a C% confidence interval for the population proportion p is

Point estimate ±margin of error

Ƹ± √Ƹ(1 − Ƹ)/

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4 Step Process:

Statistics Problems Demand Consistency

1. State: What parameter do you want to

estimate, and at what confidence level?

2. Plan: Identify the appropriate inference

method: check conditions.

3. Do: If the conditions are met, perform

calculations.

4. Conclude: Interpret your interval in the

context of the problem.

When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.

This condition is important due to the the fact that when sample size is less than of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.

Therefore, the capture rate will be lower than what is indicated in the confidence level.

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The capture rate will be lower than what is indicated in the confidence level.

An interval of conceivable values for a parameter is provided by a C% confidence interval. The interval is formed as a point estimate with a margin of error and is calculated from the data.

A C% confidence interval for the population proportion p when the random and large counts requirements are satisfied is 

Point estimate margin of error

Ƹ± √Ƹ(1 − Ƹ)

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4-Step Process:

1. Clarify what parameter you wish to estimate and at what level of confidence.

2. Make a plan and decide which inference technique is best. Check the circumstances.

3. If the criteria are satisfied, run the calculations.

4. Summarize: Consider your interval in light of the issue.

It is ensured that the sample size is less than 10% of the population size when creating a confidence interval for a population proportion. This requirement is crucial because observations are more likely to be independent when the sample size is smaller than the population size. Calculating the distribution's standard deviation is impossible if this condition is not satisfied. The standard deviation of the distribution cannot be appropriately calculated if this condition is not satisfied. The confidence level will be incorrect if the standard deviation is incorrect. Population parameters are less likely to be found in a confidence interval. As a result, the capture rate will be lower than what the confidence level predicts.

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The best way to report for (515 x 0.0025) is 25.86 and it is done using the concept of significant figures.

Given (515 x 0.0025) + 24.57

We are asked to report the answer in the best way. This can be done using the concept of significant figures.

We can see that 515 has 3 significant figures

0.0025 has 4 significant figures ( we have to consider the zeros after the decimal)

24.57 has 4 significant figures

Thus the best answer will have 4 significant figures.

(515 * 0.0025 ) + 24.57 = 25.8575 = 25.86

We have to round off the answer to 4 significant figures, thus it'll be 25.86 ( 5 becomes 6 because the figure next to 5 is 7, thus 5 will be rounded off to 6 )

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The solution is, the sequence is, {3, 31, 49, ..............}

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

here, we have,

t(0) = 3

and that the sum of the first three terms ( t(0), t(1) , and t(2) ) is 63

let, the 1st term = a

common difference = d

so, we have,

a = 3

and, a+ a+d + a+ 2d = 63

or, 9+ 3d = 63

or, 3d = 54

or, d = 18

Hence, The solution is, the sequence is, {3, 31, 49, ..............}

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The required angle ∠BAC is equal to 31

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here:  ∠ACB = 59° and the diameter of the circle as AC

Now since AC is diameter , When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference.

Thus ∠ABC= 1/2 × 180

                   =90

Thus ∠BAC= 180-90-59

                    = 31

Hence, The required angle ∠BAC is equal to 31

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Answer:

1 and 1

5 and 10

7 and 14

Step-by-step explanation:

you just have to multiple 2 by the number in (T)

When ΔKLM is dilated with a scale factor of 2 the new ΔK'L'M' has vertices K'(4,10), L'(8,4) and M'(4,4).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The ΔKLM has the coordinates of vertices - K(2,5), L(4,2) and M(2,2)

If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.

When the triangle is dilated with the scale factor of 2, the coordinate points formula becomes -

(x,y) → (2x,2y)

So, obtain the new triangle ΔK'L'M' -

K(2,5) → [2(2),2(5)] → K'(4,10)

L(4,2) → [2(4),2(2)] → L'(8,4)

M(2,2) → [2(2),2(2)] → M'(4,4)

The graph for the new coordinates have been ploted.

Therefore, the new coordinates are K'(4,10), L'(8,4) and M'(4,4).

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The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.

A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.

In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get

=> x=2t²-4.

To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.

when t=-1,

=> x=2(-1)²-4 = 0.

And when

t=1, x=2(1)²-4 = -2.

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The capacity of the elevator is 15 children or 11 adults. If 9 children are currently on the elevator, then there are 15 - 9 = 6 spots available for either children or adults.

However, since the maximum number of adults the elevator can hold is 11, the answer to the question is 11 - 9 = 2 adults can still get in.

You can act for the unknown amounts by the use of variables. Follow ignoring the description is and convert it one by one mathematically. For example, if it is asked to increase some item by 5, then you can add 5 in that item to increase it by 5.

If a thing is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

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