two airplanes take off from the airport at the same times heading in opposite directions. after 2 hours the planes are 1500 miles apart. if the speeds of the planes differ by 50 mph, find the speed of the slower plane

n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

Now, According to the question:

It is easy to show that a tree with  n ≥ 9 can have at most one vertex of degree n - 3. It is [tex]v_0[/tex].

Now, there are n - 1 - (n - 3) = 2 vertices that are not adjacent to [tex]v_0[/tex], it is also

[tex]v_n_-_1[/tex] and [tex]v_n[/tex]

Then a desired tree can be of 3 possible forms:

1. n - 4 out of n - 3  neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 2 and is adjacent to both [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_n_-_1[/tex] has degree 2 and is adjacent to [tex]v_k[/tex] and [tex]v_n.v_n[/tex] is a leaf.

2. n − 5  out of the n − 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_j[/tex] and [tex]v_k[/tex]. [tex]v_j[/tex]has degree 2 and is adjacent to [tex]v_0[/tex] and  [tex]v_n_-_1[/tex]. [tex]v_k[/tex] also has degree 2 and is adjacent to[tex]v_0[/tex] and [tex]v_n[/tex]. [tex]v_n[/tex] and  [tex]v_n_-_1[/tex] are both leaves.

3. n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

It is then easy to computer the number of trees in each form and sum them up.

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Answer:

46

Step-by-step explanation:

draw a line at 96° & make it parallel to bottom line

which will slice 96° into 2 angles

lower half is 180-130=50

top half is 96-50=46

angle 4r equals to top half

Answer:

That's what I got, not sure but I tried so I hope it helps.

After cost, the more money did Kevin make on Saturday than on Monday is $376.89.

The amount of Spends on monday is,

Sales = $397.35

Supply cost = $108.72

So the profit he is earning is

$397.35 - $108.72 = $288.63

The amount of Spends on Saturday is,

Sales = $914.06

Supply cost = $248.54

So the profit he is earning is

$914.06- $248.54= $665.52

Money did Kevin make on Saturday than on Monday is,

Money from saturday - money from monday

= $665.52 - $288.63

= $376.89

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.

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Answer:

39°

Step-by-step explanation:

Information we need to know

As we know, one of the angles in this triangle is 39° this means that the angle opposite it would also be 39°! This is because as the triangle is SAS v and the given 39 has to be equal

Have a lovely day :)

Answer:

39°

Step-by-step explanation:

Triangle HJI is an isosceles triangle.

In isosceles triangles the base angles are congruent which means their measures are equal.

So the measure of m∠HIJ = 39°

The exact length of line segment PQ is 22.4.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

Given;

p(x,y)=(17,4)

m(x,y)=(-2,16)

Now,

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

D^2= (-2-17)^2+(16-4)^2

D^2=361+144

D^2= 505

D=22.4

Therefore, the distance will be 22.4

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The standard parameterization for the tangent line  is x = 12t + 18 , y = 3t + 13 , z = 54t + 54

Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.

Given that,

Given that, t = t0 = 3, I + (3t + 4) j + (2t 3) k

In order to get the tangent line to the curve at t=3, (x, y, z) = 18, 13, and 54,

r'(t) = 4t, 3, > and r'(t=3) = 12, 3, 54>. (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

The tangent line's usual parameterization is as follows:

x=12t+18, y=3t+13, and z=54t+54

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The width of the box of books which Mr. Lin recieved which is in the shape of Rectangular Prism is (486/l*h) units.

A three-dimensional solid form having six sides, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

According to the face form or the angle the faces make with the base, there are two different varieties of rectangular prisms.

Below are several characteristics of a rectangular prism that make it simple to recognize one.

The length of the rectangular Prism is l.

Width is w , height is h

Therefore,

Volume (V) = lbh

We know Volume is 486

so we casn find the width of the rectangular prism as 486/lh

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The process of converting repeating, non-terminating decimal to a fraction has been explained below. On conversion of 0.1515…, we get the fraction as 5/33.

What is a non-terminating decimal?

Non-terminating decimals are those decimal numbers that never reach an end since there is no endpoint in their decimal digits.

We are given a repeating, non-terminating decimal as 0.1515…

So, let x = 0.1515151515  ...(1)

Here, .15 is repeating

So, we will move one set of the repeating digits in front of the decimal.

By this, we get

100x = 15.1515151515     ...(2)

Now, on subtracting (1) from (2), we get

⇒100x - x = 15.1515151515 - 0.1515151515

⇒99x = 15

⇒x = 15/99

⇒x = 5/33

Hence, this way we can convert repeating, non-terminating decimal to a fraction.

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Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

The actual distance (in miles) between her town and the state capital is 90 miles.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, a map of the state where your friend lives has the scale 1/2 in : 2 mi.

Now, 10 ÷ 1/2

= 10×2

= 20

Her measurement was 4 1/2 =9/2 inches.

Now, 20×9/2

= 90 miles

Therefore, the actual distance (in miles) between her town and the state capital is 90 miles.

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"Your question is incomplete, probably the complete question/missing part is:"

A map of the state where your friend lives has the scale 1/2 in : 2 mi.

Your friend measured the distance between her town and the state capital on the map. Her measurement was 4 1/2 inches. Based on your friend's measurement ,what is the actual distance (in miles) between her town and the state capital?

The of sin^2-cos^2 = [tex]Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

The sine of the angle is the ratio of the hypotenuse, or the angle's opposite, to the perpendicular in a right-angled triangle. Sinus is defined as Sinus = Perpendicular / Hypotenuse.

Sin 180 has a value of 0 precisely. One of the fundamental trigonometric functions is sine, which may be used to calculate the angle or sides of a right-angled triangle. Another name for it is trigonometric ratio.

If theta is an angle, then sine theta is the ratio of a right triangle's hypotenuse to its perpendicular.

trigonometric double angle formulas,

[tex]Sin 2x = 2 sin x cos x[/tex] ————(i)

And,

[tex]Cos 2x = Cos2x - Sin2x[/tex]

[tex]= 2 cos2x - 1 [Since Sin2 x + Cos2 x = 1][/tex]             ————(ii)

[tex]= 1 - 2Sin2x[/tex] ————(iii)

Now, multiply equation I by (ii) or (ii) by equation I to obtain the value of Sin 2x Cos 2x (i)

Think about equation I and (ii),

[tex]Sin 2x = 2 sin x cos x[/tex]

And,

[tex]Cos 2x = 2 cos2x - 1[/tex]

Simplifying the above equation, then we get

[tex]Sin 2x Cos 2x = 2 Sin x Cos x (2 cos2x - 1)= 4 Sin x Cos3 x - 2 Sin x Cos x= 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

Think about equation I and (iii),

[tex]Sin 2x = 2 sin x cos xCos 2x = 1 - 2 Sin2x[/tex]

Simplifying the above equation, then we get

[tex]Sin 2x Cos 2x = 2 Sin x Cos x (1 - 2 Sin2x)= 2 Sin x Cos x - 4 Sin3 x Cos x= 2 Cos x (Sin x - 2 Sin3 x)So,Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]

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Answer:

118000

Step-by-step explanation:

cash out flow = beg balance - end balance

= 24 -14 =10K

128K - 10K =118K

actual pay out is 118K

Answer:

25 minutes

Step-by-step explanation:

5/12×60 minutes

5×60=300

300/12

Answer =25

Answer:

x = -39

-39 + 27 = -12

Step-by-step explanation:

Hope it helps! =D

Answer:

Here you have

Step-by-step explanation:

x + 27 = -12

x= -12 - 27

x= - 39

Janet hiked a distance of 2.5 miles which is equivalent to 4 km

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

Speed is the ratio of total distance to total time travelled. It is given by the equation:

Speed = distance / time

Janet hiked 2.5 miles in one hour. Hence:

Speed = distance / time = 2.5 miles / one hour = 2.5 miles per hour

1 mile = 1.609 km

2.5 miles = 2.5 miles * 1.609 km per mile = 4 km

Janet hiked 4 km

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To find the total monthly mortgage payment, we need to calculate the monthly payments for both the first (80%) and second (20%) mortgages and then add them together.

First, we'll find the monthly payment for the first mortgage:

Loan amount: $140,000 x 80% = $112,000

Interest rate: 4.75% / 12 months = 0.0395%

Loan term: 30 years x 12 months/year = 360 months

Monthly payment: $112,000 * (0.0395% / (1 - (1 + 0.0395%)^-360)) = $527.64

Next, we'll find the monthly payment for the second mortgage:

Loan amount: $140,000 x 20% = $28,000

Interest rate: 7.525% / 12 months = 0.0627%

Loan term: 30 years x 12 months/year = 360 months

Monthly payment: $28,000 * (0.0627% / (1 - (1 + 0.0627%)^-360)) = $184.07

Finally, we'll add the monthly payments for both mortgages to get the total monthly payment:

Total monthly payment: $527.64 + $184.07 = $711.71

So, the total monthly mortgage payment for Pablo's house is $711.71.

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The depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units is 15000.

Cost of machine = Rs. 1,70,000; Scrap value = Rs. 20,000;

Depreciation in production during the first year =  6,000 units;

Production units during the life of the machine = 60,000 units

Depreciation rate per unit = (Rs. 1,70,000 -  Rs. 20,000)/ 60,000 units

=  Rs. 2.5

Depreciation of first year =  6,000 * Rs. 2.5 = Rs. 15,000

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Complete question

If the original cost of a machine is Rs. 170,000, estimated scrap value Rs. 20,000, what is the depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units.

Answer:

9 : 7

Step-by-step explanation:

given the ratio

4.5 : 3 [tex]\frac{1}{2}[/tex] , that is in decimal form

4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )

= 45 : 35 ( divide both parts by 5 )

= 9 : 7 ← in simplest form

Answer:

9:7

Step-by-step explanation:

Convert all the numbers to either decimal or fraction. The operation becomes simple.

Simplifying after converting to decimal

Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2

1/2 = 0.5

3 + 1/2 = 3 + 0.5 = 3.4

Ratio 4.5:3.5 = 4.5/3.5

Divide by 5 to give
[tex]\dfrac{4.5 /5 }{3.5/5} = 0.9/0.7\\\\[/tex]

Multiply both numerator and denominator by 10
0.9 x 10 = 9

0.7 x 10 = 7

So the ratio becomes 9/7 = 9:7

Simplifying after converting to fraction

4.5 = 4 + 0.5

0.5 = 1/2

5.5 = 4 + 1/2 = 4 1/2

Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2

Convert 3 1/2 to fraction

3 1/2 = (3 x 2 + 1)/2 = 7/2

So 4.5 : 3 1/2 = 9/2 : 7/2

Multiplying by 2 we get the same answer: 9:7

Choose whichever approach you feel comfortable with

The independent variable in this relationship is the radius (r) and the dependent variable is the circumference (C). This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.

Step-by-step explanation given below

Step 1: The rule states that the relationship between the circumference (C) and the radius (r) is C = 6.3r.

Step 2: This means that the circumference of a circle is a function of its radius.

Step 3: The independent variable in this relationship is the radius (r) because it is what is used to determine the circumference.

Step 4: The dependent variable in this relationship is the circumference (C) because it is what is being determined by the radius.

This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.

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Answer:

Howdy so if you buy an item to which 6% tax is added, you pay 106% of the price. The price of the item is $50, you pay 50(1.06) = $53.

You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

Determine the range of the data: 0.6 to 4.7.

Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.

Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.

Count the number of data values that fall into each class and record it in a table.

Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.

After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

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The solution to the system is x1 = -4, x2 = 10.

What is the solution to the system?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions to the system. (5, 4) is a solution of the first equation, but not the second.

The given system can be converted to an augmented matrix as follows:

[ 2 1 | 2 ]

[-1 -1 -1 | 6 ]

To find all solutions, we will reduce the system to echelon form and back substitute.

Step 1: Echelon Form

We can perform row operations to reduce the matrix to echelon form:

[ 2 1 | 2 ] R1 = R1 * 1/2

[-1 -1 -1 | 6 ]

[ 1 1/2 | 1 ] R2 = R2 + R1

[ 0 -3/2 -1 | 5 ]

Step 2: Reduced Row Echelon Form

Next, we can perform additional row operations to reduce the matrix to a reduced row echelon form:

[ 1 1/2 | 1 ] R2 = R2 * 2

[ 0 1 | 10 ]

The reduced row echelon form of the matrix represents the system of equations in a simplified form and the solution to the system can be obtained by back substituting.

Step 3: Back Substituting

x2 = 10

x1 = 1 - 1/2 x2 = 1 - 1/2 * 10 = 1 - 5 = -4

Therefore, the solution to the system is x1 = -4, x2 = 10.

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The mean in the above distribution is 1.84

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

The figure

The mean value is then calculated as

Mean = SUm of the product of children and familes/Sum of families

So, we have

Mean = (0 * 23 + 1 * 19 + 2 * 29 + 3 * 9 + 4 * 20)/(23 + 19 + 29 + 9 + 20)

Evaluate

Mean = 1.84

Hence, the mean is 1.84

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The value of the constant in the function is c  = -√3π²/6(3-π).

A differential equation is an equation that relates an unknown function and one or more of its derivatives. The equation dy/dx = f(x) is a simple example of a differential equation. Solving this equation means finding a function y with a derivative f. Therefore, the solutions of dy/dx are the antiderivatives of f. If F is one antiderivative of f, every function of the form y = f(x) + c is a solution of that differential equation.

Initial-value problems arise in many applications. Next we consider a problem in which a driver applies the brakes in a car. We are interested in how long it takes for the car to stop. Recall that the velocity function v(t) is the derivative of a position function s(t), and the acceleration a(t) is the derivative of the velocity function. In earlier examples in the text, we could calculate the velocity from the position and then compute the acceleration from the velocity. In the next example, we work the other way around. Given an acceleration function, we calculate the velocity function. We then use the velocity function to determine the position function.

The given equation is xy = y + x² sinx

⇒ xy - y =  x² sinx

⇒ y(x-1) =  x² sinx

⇒ y =  x² sinx/(x-1) +c

Also, y(π/3) = 0

Put x = π/3 in above equation:

y(π/3) =  (π/3) ² sin(π/3) /((π/3)-1)  + c = 0

After solving the above equation, we get c  = -√3π²/6(3-π)

Thus, the value of the constant in the function is c  = -√3π²/6(3-π).

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The measure of angles becomes:

∠a = 30°

∠b = 60°

∠c = 105°

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

∠a and 30° are vertical angles and vertical angles are equal

∠a = 30°

We have a triangle with a, b and a right angle. Triangles have angles that add to 180°.

∠a + ∠b + 90° = 180°

30° + ∠b + 90° =180°

120° + ∠b = 180

∠b = 180° - 120°

∠b = 60°

Angle c and 70 form a straight line and straight lines are 180 degrees

∠c + 75° = 180°

∠c = 180° - 75°

∠c = 105°

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The rate of change for a graph passing through (0, 0) and (2, -180) is -90 pieces of candy per day

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Let y represent the total pieces of candy remaining after x days. Let us assume that the graph passes through (0, 0) and (2, -180). Hence:

[tex]Slope(rate\ of\ change) = \frac{y_2-y_1}{x_2-x_1}\\ \\substituting:\\\\slope=\frac{-180-0}{2-0} =-90[/tex]

The rate of change is -90 pieces of candy per day

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