Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2

Answer:

Therefore, if Derrick wants to spend a maximum of $50 and he intends to buy a maximum of 8 tacos, then the general admission option is the cheapest. If he intends to buy 9 or more tacos, then the VIP option is the cheapest.

Step-by-step explanation:

To determine how many tacos Derrick must buy for each pricing option to be the cheapest, we can set up separate equations for each pricing option based on the total cost. Let's assume Derrick wants to spend a maximum of $50 on admission and tacos.

For the general admission option:

Total cost = 15 + 4x, where x is the number of tacos

We want to find the value of x that makes the total cost the same or less than $50:

15 + 4x ≤ 50

4x ≤ 35

x ≤ 8.75

For the VIP option:

Total cost = 36 + 1.5x, where x is the number of tacos

We want to find the value of x that makes the total cost the same or less than $50:

36 + 1.5x ≤ 50

1.5x ≤ 14

x ≤ 9.33

The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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Evaluating the piecewise function we will get:

g(-1) = -2

g(2) = 0

g(3) = 1/2

To evaluate the piecewise function we need to use the correct part depending on the domains.

g(-1), here x = -1, then we need to use the second part of the function:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2

For the second one x = 2, we use the last part:

g(2) = (1/2)*2 - 1 = 0

For the last one, we have x = 3, again we need to use the last part:

g(3) = (1/2)*3 - 1 = 3/2 - 2/2 = 1/2

These are the 3 values.

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The solution to the system of equations is x = 2 and y = -1.

To solve the system of equations:

2x - 5y = 9 ...(1)

3x + 4y = 2 ...(2)

Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':

8x - 20y = 36 ...(3)

15x + 20y = 10 ...(4)

Adding equation (3) and equation (4), the 'y' terms cancel out:

(8x - 20y) + (15x + 20y) = 36 + 10

23x = 46

Dividing both sides of the equation by 23, we find:

x = 2

Plugging the value of 'x'

2(2) - 5y = 9

4 - 5y = 9

Subtracting 4 from both sides of the equation:

-5y = 9 - 4

-5y = 5

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1.

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Answer: The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

The man rotated the window by 45 degrees and covered one of the diagonals, resulting in a smaller square window with sides measuring 1 meter.

The man achieved the transformation of his square window by dividing it into two equal halves and boarding up one of them.

Let's analyze the steps he took to accomplish this:

Initially, the man had a square window with sides measuring 1 meter

This means that the window had an area of 1 square meter (1m x 1m = 1m²).

To reduce the amount of light coming through the window, the man decided to board up half of it.

This implies that he covered one of the equal halves of the square window, while leaving the other half open.

By boarding up half of the window, he effectively blocked off half of the area of the square window.

Since the original window had an area of 1 square meter, boarding up half of it reduces the effective area to 1/2 square meter (1m² ÷ 2 = 1/2m²).

The remaining open half of the window still retains its square shape, with sides equal to 1 meter.

Therefore, the man ends up with a square window that measures 1 meter in height and 1 meter in width, but with an area of only 1/2 square meter.

In summary, the man achieved the transformation by boarding up half of the square window, effectively reducing its area to half of the original size while maintaining the same dimensions for the remaining open half. This manipulation allows him to control the amount of light entering his house while preserving the square shape of the window.

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Answer:

Option C y = -4x + 9

Step-by-step explanation:

            The line l bisects BC. The line l passes through the midpoint of BC.

B(1, 4) ; C(3 , -2)

  [tex]\sf Midpoint \ of \ BC = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

                           [tex]\sf = \left(\dfrac{1+3}{2},\dfrac{4-2}2{}\right)\\\\\\=\left(\dfrac{4}{2},\dfrac{2}{2}\right)\\\\\\=(2 , 1)[/tex]

Line l passes through (2,1) and A(3 , -3),

    [tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                [tex]\sf =\dfrac{-3-1}{3-2}\\\\\\=\dfrac{-4}{1}\\\\=-4[/tex]

m = -4

Equation of line in slope intercept form: y =mx +c

Here, m is the slope and c is the y-intercept.

        y = -4x + c

    As the line l is passing through (2,1), substitute the point (2,1) in the above equation and find c.

        1 = -4*2 + c

        1 = -8 +  c

  1 + 8 = c

        c = 9

Equation of the line l:

       y = -4x + 9    

The number of new health units is 937, and the number of improved health units is 1,137.

The number of improved health units exceeds the new ones by 200. In other words, I = N + 200.

We also know that the total number of health units counted in the report is 2,074.

Therefore, we have the equation N + I = 2,074.

Substituting the value of I from the first equation into the second equation, we can solve for N:

N + N + 200 = 2,074

2N + 200 = 2,074

2N = 1,874

N = 937

Now, we can substitute the value of N back into the first equation to find I:

I = N + 200

I = 937 + 200

I = 1,137

Therefore, the number of new health units is 937, and the number of improved health units is 1,137.

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Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

The required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex] .

Given that if  [tex]\int\limits {f(g(x)) g'(x)} \, dx[/tex]  then u = g(x) and du = g'(x),

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]  and [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

To find u and du by using the integral property

[tex]\int\limits {f(g(x)) g'(x)} \, dx = f(g(x))[/tex].

Consider  [tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx = \int\limits {\frac{1}{\sqrt{x^2+1} } } \,x dx[/tex]

That implies, u = g(x) = [tex]x^{2}[/tex] + 1.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( [tex]x^{2}[/tex] + 1 )

du = 2x + 0.

du = 2x.

Consider  [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {tan^2 x sec^2 x} \, dx = \int\limits {(tanx)^2 sec^2 x} \, dx[/tex]

That implies, u = g(x) = tanx.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( tanx )

du = [tex]sec^2 x[/tex].

du = [tex]sec^2 x[/tex].

Hence, the required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex].

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The triangle ∆DEF is similar by the SSS similarly to the triangle ∆JKL

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

To know if the triangles DEF and JKL are similar, we check if their sides corresponds in the same ratio, that is;

JK/DE = KL/EF = JL/DF

JK/DE = 9/12 = 3/4

KL/EF = 18/24 = 3/4

JL/DF = 12/16 = 3/4

Therefore, the triangle ∆DEF is similar by the SSS similarly to the triangle ∆JKL

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Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

Answer:

[tex] {x}^{ - \frac{5}{3} } = \frac{1}{ {x}^{ \frac{5}{3} } } = \frac{1}{ \sqrt[3]{ {x}^{5} } } [/tex]

The value of probability P (A or B) is,

⇒ P (A or B) = 45

We have to given that;

To find the probability that either event will occur.

Now, By given figure we get;

P (A) = 25 + 5

P (A) = 30

P (B) = 5 + 15

P (B) = 20

P (A and B) = 5

Since, The formula is,

⇒ P (A or B) = P (A) + P (B) - P (A and B)

Substitute all the values we get;

⇒ P (A or B) = 30 + 20 - 5

⇒ P (A or B) = 50 - 5

⇒ P (A or B) = 45

Therefore, The value of probability P (A or B) is,

⇒ P (A or B) = 45

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Answer: 97 degrees

Step-by-step explanation: 180-83=97

The boy is 630 meters south from his starting point.

We must take into account the southward component of his shift.

We can imagine a right-angled triangle where the hypotenuse represents the boy's total displacement of 1260 meters, the angle between the hypotenuse and the south direction is 120°, and the side next to the angle represents the southward displacement given that the boy walks 1260 meters on a bearing of 120°.

We can use trigonometric functions to calculate the displacement to the south. Since the adjacent side and hypotenuse of a right triangle are connected in this instance, we will use the cosine function.

cos(120°) = adjacent / hypotenuse

cos(120°) = adjacent / 1260

Solving for the adjacent side (southward displacement):

adjacent = cos(120°) * 1260

adjacent = (-0.5) * 1260

adjacent = -630

The negative sign indicates that the southward displacement is in the opposite direction or "south" relative to the starting point.

Therefore, the boy is 630 meters south from his starting point.

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The equation m(x) = (x-3)(x+5) is written in intercept form.

The equation m(x) = (x-3)(x+5) represents a quadratic function.

Analysing the equation.

Standard form of a quadratic equation is written as:

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Intercept form of a quadratic equation is written as:

f(x) = a(x-p)(x-q), where a, p, and q are constants representing the x-intercepts.

Vertex form of a quadratic equation is written as:

f(x) = a(x-h)^2 + k, where a, h, and k are constants representing the vertex coordinates.

The factors (x-3) and (x+5) represent the x-intercepts of the quadratic function.

Therefore, the equation m(x) = (x-3)(x+5) is written in intercept form.

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The value of x in the triangle is 9, the volume of the cylinder is 1272.3 yd³ and the volume of the sphere is 268.1 mi³.

To solve for the value of x in the triangle, we use ratio:

[tex]\frac{20}{20 + 16}=\frac{45}{45 + 3x + 9}[/tex]

Simplify and solve for x:

20/36 = 45/(3x + 54 )

Cross mulltiply:

20( 3x + 54 ) = 36 × 45

60x + 1080 = 1620

60x = 1620 - 1080

60x = 540

x = 540/60

x = 9

Therefore, the value of x is 9.

Option A) 9 is the correct answer.

Question 2)

Height of ctlinder h = 5 yd

Diameter = 18 yd

Radius = diameter/2 = 18/2 = 9 yd

Volume of cylinder = π × (radius)² × height

Volume = π × 9² × 5

Volume = 1272.3 yd³

Therefore, the volume of the cylinder is 1272.3 yd³.

Option B) 1272.3 yd³ is the correct ansswer.

Question 3)

Radius of the sphere r = 4 mi

Volume = ?

Volume = 4/3 × π × ( radius )³

Volume = 4/3 × π × ( 4 )³

Volume = 268.1 mi³

Therefore, the volume of the sphere is 268.1 mi³.

Option B) 268.1 mi³ is the correct answer.

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The calculated values of the expected values are E(2x) = 8/3 and E(x²) = 2

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

f(x) = 0.5x, 0 < x < 2

The expected value of 2x is calculated as

E(2x) = ∫2x * f(x) dx

So, we have

E(2x) = ∫2x * 0.5x dx

Evaluate

E(2x) = ∫x² dx

Integrate the function

So, we have

E(2x) = x³/3

Using the boundaries, we have

E(2x) = (2 - 0)³/3

Evaluate

E(2x) = 8/3

The expected value of x² is calculated as

E(x²) = ∫x² * f(x) dx

So, we have

E(x²) = ∫x² * 0.5x dx

Evaluate

E(x²) = ∫0.5x³ dx

Integrate the function

So, we have

E(x²) = 0.5x⁴/4

Using the boundaries, we have

E(x²) = 0.5 * (2 - 0)⁴/4

Evaluate

E(x²) = 2

Hence, the expected values are E(2x) = 8/3 and E(x²) = 2

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Answer:

(a)2030

Step-by-step explanation:

I'm assuming the 100 at the end of the question is a typo.
In 2040, the son's age can be written as [tex]\frac{x}{3}[/tex], where x equals the age of his father. In 2050, the son's age can be written as [tex]\frac{x-10}{2}[/tex] (as ten years is added between 2040 and 2050). When equated to each other--> [tex]\frac{x-10}{2}[/tex] = [tex]\frac{x}{3}[/tex], we can first simplify by multiplying both sides to reach the least common denomination 6, giving us 3(x-10)=2x --->3x-30=2x--->x=30 is the dad's age. The son's age in 2040, 30/3, is equal to 10 years, meaning he was born in the year 2030 (a).

[tex]2\cdot20\text{ m}\cdot n+2\cdot20\text{ m}\cdot 5\text{ m}+2\cdot 5\text{ m}\cdot n=1100\text{ m}^2\\40n\text{ m}+200\text{ m}^2+10n\text{ m}=1100\text{ m}^2\\50n\text{ m}=900\text{ m}^2\\n=18\text{ m}[/tex]

Answer: 180

Step-by-step explanation:

Use the order of operations: PEMDAS

Parenthesis

Exponents

Multiplication/Division

Addition/Subtraction

3² x (-2)³ x 5               >There is nothing to simplify within parenthesis

                                   >Exponents are next in Order of Operations

(3)(3) x (-2)(-2) x 5       >This is the exponents expanded

9 x 4 x 5                      >Multiply from left to right

36 x 5

180

[tex]X'=\varepsilon\setminus X[/tex] where [tex]\varepsilon[/tex] is the universe. It means that [tex]X'[/tex] is everything except the set [tex]X[/tex], and that in shown in the image C.

Only Priya's statement is correct based on the expected value. The expected value of X represents the average or mean number of successful free-throws that the player makes. Therefore, it is correct to say that the probability of making a free-throw is 0.80 on average. Hadley's statement about the next set of 2 free-throws is incorrect because the expected value does not tell us exactly how many free-throws the player will make in a given set, but rather what the average or expected number of successful free-throws will be over a series of trials.

De acuerdo con la información, el tipo de estudio de caso descrito es estudios de caso mixtos debido a que son aquellos que combinan características cualitativas y cuantitativas.

Los estudios de caso mixtos se caracterizan por combinar características cualitativas y cuantitativas en la recopilación y análisis de datos. Estos estudios buscan obtener una comprensión más completa y profunda del fenómeno estudiado.

ENGLISH VERSION

According to the information, the type of case study described is mixed case studies because they are those that combine qualitative and quantitative characteristics.

The mixed case studies are characterized by combining qualitative and quantitative characteristics in the compilation and analysis of data. These studies seek to obtain a more complete and profound understanding of the phenomenon studied.

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The expressions are simplified to;

a. 4pq

b. t³

Algebraic expressions are defined as expressions that are made up of terms, variables, coefficients, factors and constants.

These algebraic expressions are also made up of mathematical or arithmetic operations, such as;

From the information given, we have that;

The expressions are;

1.  p x q x 4

Multiply the terms, we have that;

4qp

2.t x t x t

Multiply the terms, we get;

t³

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Answer:

2

3

5

5

7

13

14

17

21

31

52

Step-by-step explanation:

but I think the town & is the best. I am not coming out of my reward.. this will be the last one day.. this will not go on. I am not coming to the office until tomorrow as I'm working for, and if I don't get any of that, I'll break it up with a choice. I am a bit worried, so I was 165 2762

Answer: Factor the problem

Step-by-step explanation:

Take out the common factor (-16), it will leave you with (t^2 - t - 30)

Factor (t - 6) (t + 5)

t - 6 = 0 or t + 5 = 0

t = 6 seconds

Answer:

55°

Step-by-step explanation:

if angle 4 = 105°, then angle 3 must be 180 - 105 = 75° (angles in straight line add up to 180°).

angles in a triangle also add up to 180°.

so we expect angle 2 to be 180 - angle 6 - angle 3

= 180 - 50 - 75

= 55°.

The estimated height of the older snail's shell is approximately 13 centimeters.

To estimate the height of the older snail's shell, we can use the concept of proportional relationships between the heights and volumes of the snail shells.

Let's denote the height of the older snail's shell as "h" (in centimeters). We can set up a proportion based on the relationship between the heights and volumes of the snail shells:

(height of younger snail) / (volume of younger snail) = (height of older snail) / (volume of older snail)

Substituting the given values:

3.9 / 3 = h / 10

To solve for "h," we can cross-multiply and then divide:

3 * h = 3.9 * 10

3h = 39

h = 39 / 3

h ≈ 13

The estimated height of the older snail's shell is approximately 13 centimeters.

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