Two buses leave a station at the same time and travel in opposite directions. One bus travels 8 mih slower than the other. If the two buses are 432 miles apart after 3 hours, what is the rate of each bus?

The ROE (return on equity) for this project if it produces an EBIT (earnings before interest and taxes) of $140,000 is given by A = 15 %

Given data ,

The Return on Equity (ROE) is calculated as the ratio of Net Income to Equity. Net Income is the EBIT (earnings before interest and taxes) minus the taxes, and Equity is the total assets minus the debt.

EBIT = $140,000

Tax rate = 25%

Total assets = $700,000

Debt = 0% (since the project is financed with 100% equity)

Taxes = Tax rate x EBIT

Taxes = 0.25 x $140,000

Taxes = $35,000

And , the net income is

Net Income = EBIT - Taxes

Net Income = $140,000 - $35,000

Net Income = $105,000

Now , the ROE is given by

ROE = (Net Income / Equity) x 100%

ROE = (Net Income / Total assets) x 100%

ROE = ($105,000 / $700,000) x 100%

ROE = 15%

Hence , the ROE is 15 %

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Answer:

The height of the kite is 63.40 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 63.40 feet.

The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)

The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.

The solution can be expressed as a piecewise-defined function:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

We have,

a.)

To find the Laplace transform of the solution, we first take the Laplace transform of both sides of the differential equation using the initial value theorem, which states that the Laplace transform of the derivative of a function y(t) is sY(s) - y(0):

s²Y(s) - s y(0) - y'(0) - 5(sY(s) - y(0)) = e^{-s}

Simplifying and solving for Y(s), we get:

Y(s) = (7 + e^{-s}/s) / (s² - 5s)

b.)

To obtain the solution y(t), we use partial fraction decomposition to separate Y(s) into two terms:

Y(s) = A/(s-5) + B/s + C/(s-5)^2

Multiplying both sides by the denominator, we get:

7 + e^{-s}/s = A(s-5)² + Bs (s - 5) + C(s)

Setting s = 0, we get:

7 = 25A - 5B + 0C

Setting s = 5, we get:

7 + e^{-5}/5 = 0A + 5B + 5C

Taking the derivative with respect to s and setting s=0, we get:

0 = 10A - B

Solving these equations, we get:

A = -1/25

B = -2/5

C = 6/25

Therefore, the solution y(t) is:

y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25

Where u(t) is the unit step function.

c.)

The solution can be expressed as a piecewise-defined function as follows:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

At t = 1, there is a discontinuity in the first derivative of the solution due to the presence of the delta function in the original differential equation.

This causes a sudden jump in the slope of the graph of the solution.

Thus,

The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)

The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.

The solution can be expressed as a piecewise-defined function as:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

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The outputs for industries X and Y will be 31 million and 43.2 million, respectively  supposedly the final demand changes to 20 for X and 30 for Y.

We will  start with industry X.

The final demand for X hade an increment from 14 million to 20 million with  an increase of 6 million, hence the final output of X must also increase by 6 million to make up for demand.

Users    Final    Producers

Demand     X          Y

X          14         7

Y           6        18

Total     20        25

The table tells us that for every additional million of final demand for X, the producers in industry X need to produce 0.5 million of output.

So the new total output for industry X is 28 + 3 = 31 million.

For  industry Y

The same scenario occurred for Industry Y which had final output of 12 in order to meet the demand increment.

So the new total output for industry Y is 36 + 7.2 = 43.2 million.

In conclusion, the outputs for industries X and Y will be 31 million and 43.2 million, respectively, if the final demand changes to 20 for X and 30 for Y.

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To draw the graph of y = g(-x), we need to replace x with -x in the original function.

If y = g(x) is given by the following graph:

(see attachment labeled "Attachment1")

Then y = g(-x) can be obtained by reflecting the graph of y = g(x) about the y-axis:

(see attachment labeled "Attachment 2")

Therefore, the graph of y = g(-x) is the reflection of the graph of y = g(x) about the y-axis.

I hope this helps you! Mark brainliest if you can :D

Yes, data provide convincing evident that contest has increased participation.

We have,

H₀: p = 0.12

Hₐ: p > 0.12

So, z = (p' - p)/ (√pq/n)

z = 1/6 - 0.2/ √(0.12 x 0.88) /210

z= 2.08

The test is right tailed.

So, P value = P( z> 2.08) = 0.0188

and, P- value < α, Reject H₀

Yes, data provide convincing evident that contest has increased participation.

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The measure of inverse of sinθ is c/√ (c² - a²)..

The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.

Mathematically, the trig identities are represented using the following method;

SOH CAN TOA

SOH is for sine θ

CAH is fof cos θ

TOA is for tan θ

From the diagram we need find the value of the opposite side;

b = √ (c² - a²)

Sin θ = b/c

The inverse of b/c = c/b

1/sinθ = c/b = c/√ (c² - a²).

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Answer:

[tex]x^2+y^2 = 2x - 2y}[/tex]

Third answer option

Step-by-step explanation:

We are given the polar equation as
[tex]r = 2(\sin \theta - \cos \theta)[/tex]
and asked to convert it into rectangular form

We have the following equations which relate (r, θ) in polar form to (x, y) in rectangular form

[tex]\cos \theta=\dfrac{x}{r} \rightarrow x=r \cos\theta\\\\\sin \theta=\dfrac{y}{r} \rightarrow y=r \sin \theta\\\\[/tex]

[tex]r^2=x^2+y^2[/tex]

Original polar equation:
[tex]r = 2(\sin \theta - \cos \theta)[/tex]

Expand the right side:
[tex]r = 2\sin \theta - 2\cos \theta[/tex]

Substitute for sinθ and cosθ in terms of x and y
[tex]r & = 2\left(\dfrac{y}{r} - \dfrac{x}{r}\right)\\[/tex]

Multiply both sides by r:

[tex]r^2 = 2(x - y)\\r^2 = 2x - 2y\\[/tex]

Substitute [tex]r^2=x^2+y^2[/tex] on the left side:
[tex]\boxed{x^2+y^2 = 2x - 2y}[/tex]

This would be the third answer opton

-1.2, earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X

Given that two machines, X and Y, produce earbuds

Let X represent the diameter of an earbud produced by machine X, and

let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm

Y has a mean of 15.2 mm with a standard deviation of 0.2 mm.

The mean of the difference, D = X - Y, can be calculated as:

mean(D) = mean(X) - mean(Y)

= 14 - 15.2

= -1.2

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The surface area of the figure is  174.7 sq. ft.

Consider the bottom rectangular surface of the figure.

The dimensions of the bottom rectangular surface are: length = 10 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₁ = length × width

A₁ = 10 × 3

A₁ = 30 sq. ft.

The dimensions of the right rectangular surface are length = 9 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₂ = length × width

A₂ = 9 × 3

A₂ = 27 sq. ft.

The dimensions of the left rectangular surface are length = 11 ft and width = 3 ft

Using the formula for the area of rectangle, the area of bottom surface of the figure would be,

A₃ = length × width

A₃ = 11 × 3

A₃ = 33 sq. ft.

There area two parallel triangular suface with dimensions: base = 11 ft and height = 7.7 ft

Using the formula of the area of triangle the surface area of these two triamgular surfaces would be,

A₄ = 2 × 1/2 × base × height

A₄ = base × height

A₄ = 11 × 7.7

A₄ = 84.7 sq. ft.

So, the total surface area of the figure would be,

A = A₁ + A₂ + A₃ + A₄

A = 30 + 27 + 33 + 84.7

A = 174.7 sq. ft.

This is the required surface area of the figure.

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

When a tank is 1/2 full it contains 45 liters of water, the area of the base is 450 cm², the height of the tank is 200 cm.

Let the height of the tank be 'h' cm. Since the tank is half full, it contains 45 liters of water which is equal to 45,000 cubic cm.

The volume of water in the tank is given by:

Volume of water = (1/2) x (450 cm²) x (h cm)

Since the volume of water is 45,000 cubic cm, we can set up the following equation:

(1/2) x (450 cm²) x (h cm) = 45,000 cubic cm

Simplifying, we get:

225h = 45,000

h = 200 cm

In this case, the area of the base is given in square centimeters, so we must use cubic centimeters for the volume of water. Also, we converted the liters to cubic centimeters by multiplying by 1000 since 1 liter is equal to 1000 cubic centimeters.

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The evaluated speed of P is 54.5 m s¯¹, under the condition that two forces F₁ and F₂ act on a particle P. The force F₁ is given by F₁ = (-i + 2j) N and F₂ acts in the direction of the vector (i + j).

To evaluate the speed of particle P when t = 3 seconds, we can apply the equations of motion formulas to calculate the velocity if the acceleration and initial velocity values are already given.
The formula can be derived :
v = u + at
Here,
v =  final velocity of the particle,
u = initial velocity of the particle,
a = acceleration acting on the particle
t = time taken.
It is known to us that the acceleration of P is (3i + 9j) ms² and at time t = 0, the velocity of P is (31 -22j) m s¯¹. We can evaluate the initial velocity u by taking the magnitude of (31 -22j) that is
√(31² + (-22)²)
= 39.051 m s¯¹.
Now we can staging all values into the formula
v = u + at
v = 39.051 + (3i + 9j) × 3
v = 39.051 + (9i + 27j)
v = (39.051 + 9)i + (27)j
v = 48.051i + 27j
Then, when t = 3 seconds, the speed of particle P is √(48.051² + 27²)
= 54.5 m s¯¹.
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You can use functions to complete the table as follow:

x   f(g(x))

4      2

10     4

20    6

34    8

52   10

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

f(x) = √(x+1)

g(x) = 2x - 5

When x = 4:

f(g(x)) = f(g(4))

f(g(4)) = f(2*4 - 5)

f(g(4)) = f(3)

f(g(4)) = √(3+1)      [Remember f(x) = √(x+1)]

f(g(4)) =  2

When x = 10:

f(g(10)) = f(2*10 - 5)

f(g(10)) = f(15)

f(g(10)) = √(15+1)

f(g(10)) = 4

When x = 20:

f(g(20)) = f(2*20 - 5)

f(g(20)) = f(35)

f(g(20)) = √(35+1)

f(g(20)) = 6

When x = 34:

f(g(34)) = f(2*34 - 5)

f(g(34)) = f(63)

f(g(34)) = √(63+1)

f(g(34)) = 8

When x = 52:

f(g(34)) = f(2*52 - 5)

f(g(34)) = f(99)

f(g(34)) = √(99+1)

f(g(34)) = 10

Thus, fill the values into the table to complete it.

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The length of m∠WYX is equal to 12π units.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

16π = θ(π/360) × 8²

Central angle, θ = 0.5π

m∠WYX = 2π - m∠WX

m∠WYX = 2π - 0.5π

m∠WYX = 1.5π

Length of m∠WYX = (1.5π)/2π × 2πr

Length of m∠WYX = (1.5π)/2π × 2π(8)

Length of m∠WYX = 12π units.

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The area of the base of the cylinder is 78.54 ft² and height of the cylinder is  6.31 ft.

To find the area of the base of the cylinder, we can use the formula:

A = πr²

Substituting the given value of radius, we get:

A = π(5 ft)²

A = 78.54 ft²

Therefore, the area of the base of the cylinder is 78.54 ft².

b. To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Substituting the given values of volume and radius, we get:

157.08 ft³ = π(5 ft)²h

Simplifying, we get:

h = 157.08 ft³ / (π(5 ft)²)

h = 6.31 ft

Therefore, the height of the cylinder is approximately 6.31 ft.

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The domain can be written as follows:

R - {x = n*12pi or m*4pi | n, m ∈ Z}

where pi = 3.14 and R is the set of real numbers.

Here we want to find the domain of the function:

y = tan(x/8)

The tangent is the quotient between the cosine and the sine, then we will get:

sin(x/8)/cos(x/8)

The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.

The zeros are:

cos(x/8) = 0

We know that cos(pi/2) = cos(3pi/2)  = 0

Then:

x/8 = pi/2

x = 4pi

x/8 = 3pi/2

x = 12pi

So the domain is the set of all real numbers except the ones in the next set:

{x = n*12pi or m*4pi | n, m ∈ Z}

Where Z is the set of integers.

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The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.

In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.

Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;

Fraction = 1/2 + 2/3

Fraction = (3 + 2)/6

Fraction = 5/6 cups of grapes and raisins.

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The solution to the system of equations in this problem is given as follows:

(0.6, 2.4).

The system of equations in the context of this problem is defined as follows:

Equaling the two equations, we can obtain the value of x, as follows:

4x = -x + 3

5x = 3

x = 3/5

x = 0.6.

Substituting the value of x into the second equation, we obtain the value of y as follows:

y = -0.6 + 3

y = 2.4.

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The area of the given triangle is expressed as: 25.6 in²

We are only given two sides of the triangle and an angle and so we must find the length of the third side to be able to find the area. The length of the third side is gotten from cosine rule to get:

a = √(14.1² + 7.2² - 2(14.1 * 7.2)*cos 30.3)

a = 8.68 in

In order for us to calculate the area of triangle which has 3 sides, we will have to utilize the Heron's Formula.

From the formula, the area of a triangle (A) that has 3 sides a, b, and c is calculated via the formula:

A = √[s(s - a)(s - b)(s - c)]

where:

s denotes the semi-perimeter of the specific triangle given by the formula: s = (a + b + c)/2.

s = (8.68 + 14.1 + 7.2)/2

s = 14.99 in

Thus:

Area = √[14.99(14.99 - 8.68)(14.99 - 14.1)(14.99 - 7.2)]

Area = 25.6 in²

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The length of each garden side is 4 ft.

Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.

Let s be the length of the side of the gardens,

Since, she need 3 gardens,

So,

3 × side² = 48

3s² = 48

s² = 16

s = 4

Hence, the length of each garden side is 4 ft.

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In the given triangle ABC,

i. SAS is given

ii. The law of cosine can be used to solve it.

The cosine rule is a mathematical principle that can be applied to determine the unknown length of side, or measure of the internal angle of a none right angled triangle.

The cosine rule states that;

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

Considering the given attachment to the question, for a standard labelling of triangle ABC. It can be observed that;

a. The given properties of the triangle are: Side-Angle-Side (SAS)

b. The angle given is an included angle, so that the cosine law is required to solve the triangle.

Therefore, the answer is: SAS, law of cosine

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The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range will be; 0.1487

Since the total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range is 4.7

The probability formula will be

P = required outcome / Total possible outcomes

From the information provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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Answer:

Step-by-step explanation:

A full revolution on a circle/radians is 2[tex]\pi[/tex], so keep adding or subtracting 2[tex]\pi[/tex] til you get a base angle, that's when the sign changes.  Then decide which quadrant your in.

For this one the equivalent of 2[tex]\pi[/tex] is [tex]6\pi /3[/tex]

-29[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -23[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -17[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -11[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= -5[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]

= 1[tex]\pi[/tex]/3            sign changed it's equavalent to [tex]\pi /3[/tex]  Which is in the first quadrant.   See unit circle.

-5[tex]\pi[/tex]/6 + [tex]12\pi /6[/tex]

=[tex]7\pi /6[/tex]              third quadrant,  i count quadrants by know [tex]\pi[/tex]/6 is 30°, so every 30° line is 1/6 of the unit circle.  when i count 7 of them that's in the 3rd quadrant.  Don't forget to count the axis's

2[tex]\pi[/tex]/3 is in the 2nd quadrant.  Count my pi/3's which is 60°

45[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= 31[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=17[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

=3[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7

= -11[tex]\pi[/tex]/7      1/7th's is not your typical unit circle angle

This one i think of logically.  this is -1 4pi/7  

1 pi going backwards is 180

keep going backards 4/7 is bigger than 1/2 so it's in the 1st quadrant

Since we can't have a fractional number of lines, Citywide can sign up for a maximum of 1 line and still stay within their budget.

Let's start by calculating the total amount Citywide pays for their telephone costs without the federal excise tax. We can do this by subtracting the 3% tax from the total budget:

$190 / 1.03 = $184.47

The $96 budget plan includes 4,000 minutes, which means that each minute costs:

$96 / 4,000 = $0.024

If Citywide wants to stay within their budget, they need to make sure that the total cost of the lines they sign up for plus the federal excise tax is less than or equal to $190.

Let's represent the number of lines Citywide signs up for as "n". The total cost of the lines plus tax can then be represented as:

n * $96 * 1.03

Setting this expression less than or equal to $190, we get:

n * $96 * 1.03 <= $190

Simplifying, we get:

n <= $190 / ($96 * 1.03)

n <= 1.945

Thus, Citywide can sign up for a maximum of 1 line and still stay within their budget.

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Answer:

√50

Step-by-step explanation:

To solve, use distance formula.

√(9-4)^2 + (2-(-7))^2=

√5^2+5^2=

√50

Answer:

Step-by-step explanation:

Answer:

where is the question.

send it so I'll answer it

The ground distance of the plane is 170,138.5 ft.

The ground distance of the plane is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height attained by the plane is the opposite side, while the ground distance is the adjacent side

tan (10) = 30,000 ft/d

d = 30,000 ft/tan(10)

d = 170,138.5 ft

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If teacher has total "52 cards", and teacher gives each student "1 card" until all 52 cards are distributed, then number of students which got exactly 9 cards are (b) 4 students.

There are 6 students and 52 cards. The teacher gives each student one card until all 52 cards are given out in game. We want to know how many students receive exactly 9 cards.

To solve the problem, we divide the total number of cards (52) by the number of students (6) to find the average number of cards per student.

⇒ 52 cards / 6 students = 8.67 cards per student;

Since we can't give a student a fraction of a card, we need to round down to 8 cards,

If we give each student 8 cards, that will total of 8 cards × 6 students = 48 cards. which leaves 4 cards left over that we can't give out evenly.

This means that four-students will receive 9 cards each and two students will receive 8 cards each.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

A teacher gives 6 students some cards to play a game, She has 52 cards in total, The teacher gives each 1 card until all 52 cards are given.

How many students gets exactly 9 cards?

(a) 2

(b) 4

(c) 5

(d) 6.