In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3.

To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and

∠DFE is 4 times greater than ∠GFH.
∠FHG is One-fourth the measure of ∠FED.
∠DFE is congruent to ∠GFH.
∠FHG is congruent to ∠EFD.

Note that

108° = 90° + 18°

so

sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)

Then

sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1

by the Pythagorean identity.

The value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. The six - trigonometric functions are -

We have the following trigonometric equation -

sin²(108°) + sin² (18°) ​

We have the following expression -

sin²(108°) + sin² (18°) ​

(0.95)² + (0.31)²

0.9025 + 0.0961

0.9986

Therefore, the value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

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The amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

First step

Lease value payments after first payment:

Lease value payments=  $5,588,516- $716,000

Lease value payments= $4,872,516

Second step

Lease value payments after second payment:

Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000

Lease value payments=$4,872,516+$438,526.44-$716,000

Lease value payments=$4,595,042.44

Third step

2022 Interest revenue=$4,643,787.6×9%

2022 Interest revenue=$413,553.8196

2022 Interest revenue=$413,553.82 (Approximately)

Therefore the amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

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Answer:

center (0, 3) and radius 2√2

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex]x^2+y^2-6y+1=0[/tex]

Subtract 1 from both sides:

[tex]\implies x^2+y^2-6y=-1[/tex]

To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:

[tex]\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2[/tex]

[tex]\implies x^2+y^2-6y+9=8[/tex]

Factor the trinomial with variable y:

[tex]\implies x^2+(y^2-6y+9)=8[/tex]

[tex]\implies x^2+(y-3)^2=8[/tex]

Factor [tex]x^2[/tex] to match the general form for the equation of a circle:

[tex]\implies (x-0)^2+(y-3)^2=8[/tex]

Compare with the general form of the equation for a circle:

[tex]\implies a=0[/tex]

[tex]\implies b=3[/tex]

[tex]\implies r^2=8 \implies r=2\sqrt{2}{[/tex]

Therefore, the center is (0, 3) and the radius is 2√2

Answer:

Money Paid in Total  = $45

Step-by-step explanation:

Firstly, the term Mark-up refers to the amount added to the cost price to cover the overheads and realize a profit.

A mark-up percentage is a percentage (%) that is used as a basis to determine the mark-up value.

Given

Cost of an Item = 60$

Markup % = 25% on cost

Hence, Mark up in $ = 60$*25%

                                   = 15$

Therefore, Actual cost of an item = Cost of an item - Mark up on Item

                                                        = 60$ - 15$

                                                         = 45$

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Answer:

3x - 7

Step-by-step explanation:

This questions asks about the subtraction of functions. To find the answer, we can subtract the same way we would subtract polynomials.

Subtracting Expressions

First, set up the subtraction problem by taking the expression for f(x) and subtracting the expression equal to g(x) from it.

This looks like:

Next, distribute the negative to the second binomial

Then, combine like terms

Since we are not given a x-value, this is the final answer.

Solving for an X-Value

If you are given an x-value, the best way to solve the equation is to first solve each function and then subtract.

For example, using the same rules for each function let's solve (f-g)(2).

First, solve for f(2) and g(2)

Then, subtract the 2 values

The expression for the polynomial graphed will be y(x) = (x + 3)(x - 1 )(x - 4 ).

From the graph, the zeros of the polynomial of given graph are:

x = -3

x = 1

x = 4

Equate the above equations to zero

x + 3 = 0

x - 1 = 0

x - 4 = 0

Multiply the equations

(x + 3)(x - 1 )(x - 4 ) = 0

Express as a function gives;

y = (x + 3)(x - 1 )(x - 4 )

Hence, the factored form of the polynomial will be y = (x + 3)(x - 1 )(x - 4 ) .

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Answer: [tex]87^{\circ}[/tex]

Step-by-step explanation:

Because an angle inscribed in a semicircle is a right angle, [tex]\angle B=90^{\circ}[/tex]

So, as angles in a triangle add to 180 degrees, [tex]\angle A=180^{\circ}-90^{\circ}-3^{\circ}=\boxed{87^{\circ}}[/tex]

he value of x and y from the given figure are 49/5 and 49/15

From the given similar triangles, the following expression is true

21/30 = 7/15 = k

Also, x/21 = y/7 = 7/15

Equate

x/21 = 7/15

15x = 7 * 21

5x = 7 * 7

x = 49/5

Similarly

y/7 = 7/15

15y = 49

y = 49/15

Hence the value of x and y from the given figure are 49/5 and 49/15

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Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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Step-by-step explanation:

length = breadth + 5

the perimeter is a rectangle is

2×length + 2×breadth

in our case

2×length + 2×breadth = 74

so, we use the first equation in the second equation :

2×(breadth + 5) + 2×breadth = 74

2× breadth + 10 + 2× breadth = 74

4×breadth = 64

breadth = 16 m

length = breadth + 5 = 16 + 5 = 21 m

Answer:

[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]

[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]

[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]

Use integration by parts.

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

Substituting the defined parts into the formula:

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]

[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]

[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]

Therefore:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]

[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]

[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]

Divide both sides by 2:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]

Rewrite in the same format as the given integral:

[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Differentiation Rules used:

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]

Integration Rules used:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]

The mean will be 10.08 and the standard deviation will be 1.27.

The complete question is given below:-

The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.

Find the mean and standard deviation of this probability distribution.

For samples of size 12, what is the expected number of claims made by people under 25 years of age?

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

Given that:-

The mean will be calculated by the formula below:-

Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08

The standard deviation will be calculated as:-

Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27

Therefore the mean will be 10.08 and the standard deviation will be 1.27.

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Step-by-step explanation:

2.

the volume of the box is

length × width × height = 13×13×13 = 13³ = 2197 cm³

the ratio of the density indignation tells us that every cm³ of soil weighs 1.33 g (or every unit of 1.33g soil fits into 1 cm³).

we have 2197 cm³.

their weight is

2197 × 1.33 = 2,922.01 g

so, the filled box clearly exceeds the max. weight of the window ledge, and it is NOT safe to put it there.

b

yes, it would be a little bit less dense.

because every bit of weight you put on top of something increases the pressure on and therefore the density of that something.

Answer:

The practical domain of function is , Roscoe can ride his bike only from 10 miles to 30 miles.

Domain of function is defined as the set of input values for which the function is defined i.e.  the set of its possible inputs,

The amount of time it takes for Roscoe to ride his bike m miles is represented by a function.

Where m represent, number of miles he can ride.

Above function is defined for every value of m . But in question it is mention that Roscoe rides his bike at least 10 miles but not more than 30 miles.

Therefore, Domain of function is from 10 miles to 30 miles

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

you can use power rule of derivatives for that.

Answer:

y = - 1/4 x + 1

Step-by-step explanation:

Find two convenient integer coordinates like   -4,2 and  4, 0

  use these points to  calculate the slope to be -1/4

   intercept is b = 1

y = -1/4 x + 1

Answer:

  [tex]\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

An angle is co-terminal with the same angle that has any multiple of 360° added to it.

__

The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.

These coordinates are ...

  (x, y) = (cos(300°), sin(300°))

  (x, y) = (1/2, -√3/2)

Answer:

$12.

Step-by-step explanation:

1) if price of one doll is 'x', of one dress is 'y', then the condition 'buys one doll and one dress, it will cost her $21.00' can be written as x+y=21;

2) the condition 'buys two dolls and three dresses, it will cost her $51.00' can be written as 2x+3y=51;

3) it is possible to make up the system:

[tex]\left \{ {{x+y=21} \atop {2x+3y=51}} \right. \ = > \ \left \{ {{x=12} \atop {y=9}} \right.[/tex]

4) the price of one doll is 12$.

Answer:

Hello

DiinoMahFill in the blank. In the triangle below, x=?. Round your answer to two decimal places.

Answer: y = 4x + 5/4

Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.

Answer:

[tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]

Step-by-step explanation:

You work in the order you have: you start with your number x, so your first step will be [tex]f_0(x)=x[/tex]. then you add 2: [tex]f_1(x) =x+2[/tex]. Then you take the square root of what you have in the previous step: [tex]f_2(x) = \sqrt {x+2}[/tex]. Finally, you divide by 9: [tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]

Using Venn probabilities, the correct statement is given by:

ii) [tex]|A \cup B| = |A| + |B| - |A cap B|[/tex]

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Hence, statement ii is correct.

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Answer:

[tex](x + y)(x - y)[/tex]

[tex](3.5 - 8.7)(3.5 + 8.7)[/tex]

[tex](-5.2)( 12.2)[/tex]

[tex]-63.44 [/tex]

Step-by-step explanation:

b because you have to multiply

Answer:

1: 8 ft

2: 10 cm

3: c is approximately 127.2 or exactly equal to 90 * sqrt(2)

4: sqrt(133)

Step-by-step explanation:

(1) Kevin tries to climb a wall with a ladder. The length of a ladder is 17 feet and it reaches only 15 feet up the wall. What is the distance between the base of the ladder and the wall? :

Here you can use the Pythagorean Theorem to find the length of the base.

the equation is a^2 + b^2 = c^2 where c is the hypotenuse. In this case 17 is the hypotenuse which is c, 15 is a or b it doesn't really matter where you put it.

a^2 + (15)^2 = 17^2

a^2 + 225= 289

a^2 = 64

a = 8

(2) In a right triangle, if the length of one leg is 8 cm and the length of the other leg is 5 cm, what is the length of the hypotenuse? :

The same formula can be used except you don't have to move anything around.

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

10 = c

10 cm

A baseball field is a square with sides of length 90 feet. What is the shortest distance between the first base and the third base?:  

So if you look at the image provided, the shortest distance is just a straight line, but more specifically that straight line forms two triangles with the same lengths, That line is the hypotenuse so you can use the same equation as the previous equations

90^2 + 90^2 = c^2

16,200 = c^2

c is approximately 127.2 or exactly equal to 90 * sqrt(2)

(4) How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?:

6^2 + b^2 = 13^2

36 + b^2 = 169

b^2 = 133

b = sqrt(133)

Answer:

Question?

Step-by-step explanation:

Given that [tex]f(x) = 3x^2 + 5[/tex], we have

[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]

so that

[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]

Answer:

question 1

the ticket price which results in the greatest revenue is 14+8=22$

question 2

the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$

Step-by-step explanation:

the cost of a ticket to music concert is 14$

capacity of people for concert = 7500

for every increase in price attendance decreases by 250

so the required equation for getting revenue is
                         y =   (14+x)(7500-250x)
                            = 105000+7500x-3500x-250x^2

by differentiating the above equation with respect to x we can find the local maxima which gives us the price for getting more revenue

      dy/dx = 7500 -3500 - 500x =0

                      4000=500x

                          x= 8

from the above equation we got that if the increase in price was 8$ we will be getting the most revenue out of the concert

question 1

the ticket price which results in the greatest revenue is 14+8=22$

question 2

the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$

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