1-5 solve graphically

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The required surface area of the climbing toy is 47 square meters.

The climbing toy consists of two cubes, one larger and one smaller. The side lengths of the larger cube are 2 m, so its surface area is:

Surface area of larger cube = 6s^2 = 6(2)^2 = 24 square meters

The smaller cube has a side length of 1 m and it is resting on one entire face on the larger cube. So, the surface area of the smaller cube that is not in contact with the larger cube is:

Surface area of smaller cube = 6s² - 1s² = 6(1)² - 1(1)²= 5 square meters

Therefore, the total surface area of the climbing toy is the sum of the surface area of the two cubes, minus the area of the face where the smaller cube is in contact with the larger cube. The area of this face is the same as the surface area of one face of the smaller cube, which is 1 square meter. Thus, the total surface area is:

Total surface area = 2(Surface area of the larger cube) + Surface area of the smaller cube - Area of the face in contact

Total surface area = 2(24 square meters) + 5 square meters - 1 square meter

Total surface area = 47 square meters

Therefore, the surface area of the climbing toy is 47 square meters.

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Answer:

\(V = 208\,u^{3}\) (Option C)

Step-by-step explanation:

The volume of the composite figure is:

\(V = \frac{1}{2}\cdot (3\,u)\cdot (4\,u)\cdot (8\,u) + (5\,u)\cdot (4\,u)\cdot (8\,u)\)

\(V = 208\,u^{3}\) (Option C)

Answer:

C) 3, 4, 5

Step-by-step explanation:

The rule for Pythagorean Triple is:

\( {a}^{2} + {b}^{2} = {c}^{2} \)

3, 4, 5 is one of the most commonly known triple and it proves the triple rule since

\( { 3}^{2} + {4}^{2} = {5}^{2} \)

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer:

The medal received by an Olympic gymnast has a nominal level of measurement.

Step-by-step explanation:

The variable, X can be described as the type of medal received by an Olympic gymnast.

The values that X can take are: gold, silver and bronze.

The variable X is a qualitative variable, since it describes the different categories of winning a medal.

There are two types of qualitative variable level of measurement:

In case of nominal level of measurement, words, letters, and alpha-numeric symbols are used to denote the category.  For instance, the data about individuals belonging to three different gender categories, the data about individual’s different eye color.

Thus, the medal received by an Olympic gymnast has a nominal level of measurement.

Answer:

1.56% probability that the student gets all three questions right

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Each question has 4 possible answers, one of which is correct.

So \(p = \frac{1}[4} = 0.25\)

Three questions.

This means that \(n = 3\)

What is the probability that the student gets all three questions right?

This is \(P(X = 3)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156\)

1.56% probability that the student gets all three questions right

Answer:

They are going away from each other.

So add up their speed.

combined speed = x+x-16

=2x-16

Time = 2 hours

Distance = 400 miles

Distance = speed * time

(2x-16)* 2

4x-32=400

4x=400+32

4x=432

/12

x=108 mph west bound

east bound = 108 -16 = 92 mph

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Bob travels to ocean with an average speed of 50 miles per hour 50mi/h.

The distance from the Bob's house to ocean is 350 miles.

In order to calcuale how long will Bob travel from his house to ocean, you se the following formula:

t = v x s

t: time

v: Bob's average speed = 50mi/h

s: distance Bob's house - Ocean = 350mi

By replacing you obtain:

t

Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

Step-by-step explanation:

Answer:

Problem  says that the number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 with increments of 0.5. All the whole numbers are labeled on the number line. An empty circle is shown on the third mark to the left of 0. The region to the left of the empty circle is shaded. Graph is not given so I have created graph as per given description.

Now we have to select correct choice.

From graph we can easily see that third statement

"Yes it can, because −3.5 lies to the left of −1.5. " is correct.

Step-by-step explanation:

The answer is D

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

This distance would be written as a whole number as 93,000,000.

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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The system of equations has only one solution and is the point (1, 1)

Here we have the graph of a system of equations, where we can see that both of them are linear equations.

Whenw e have a graph of a system, the solutions are all the points where the graphs of the equations intercept.

On the given graph, we can see that the two lines intersept at the point (1, 1)

So we have only one solution and is the point (1, 1)

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The number of tablets that should be taken each day by the patient who needs Synthroid is 1 tablet.

To find the number of tablets of Synthroid that should be taken, you convert the requirements from micrograms ( μg ) to milligrams ( mg).

1 milligram = 1, 000 micrograms ( μg )

25. 0 μg in milligrams is therefore:

= 25 / 1, 000

= 0. 025 mg

This means that the number of tablet to take is:

= Mg requirement / Mg of tablet

= 0. 025 / 0. 025

= 1 tablet

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Answer/Step-by-step explanation:

✍️Slope of the line using two points, (2, 2) and (6, 10),

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 2}{6 - 2} = \frac{8}{4} = 2 \)

✍️To find the equation of the line in slope-intercept form, we need to find the y-intercept (b).

Substitute x = 2, y = 2, and m = 2 in y = mx + b, and solve for b.

2 = (2)(2) + b

2 = 4 + b

2 - 4 = b

-2 = b

b = -2

Substitute m = 2 and b = -2 in y = mx + b.

✅The equation would be:

\( y = 2x + (-2) \)

\( y = 2x - 2 \)

✍️To find the value of a, plug in (a, 8) as (x, y) into the equation of the line.

\( 8 = 2(a) - 2 \)

\( 8 = 2a - 2 \)

Add 2 to both sides

\( 8 + 2 = 2a \)

\( 10 = 2a \)

Divide both sides by 2

\( \frac{10}{2} = a \)

\( 5 = a \)

a = 5

✍️To find the value of b, plug in (4, b) as (x, y) into the equation of the line.

\( b = 2(4) - 2 \)

\( b = 8 - 2 \)

\( b = 6 \)

Answer:

B

Step-by-step explanation:

Claude owns a store. Every year, he pays corporate tax. Option B is correct.

Claude owns a store. Every year, he pays _____.
Black space to be filled from the following option,
A. sales tax B. corporate tax C. marginal tax D. personal property tax

A corporate tax is a tax levied on the net gain of an enterprise that is taxed at the commodity level in a particular mark. Net gain for corporate tax is commonly the financial statement of net gain with transformations and may be defined in detail in the tax system of each country.

Since the store owner mostly pays the corporate tax besides there, sales tax is paid by the company owners, marginal tax is also paid by the production companies, and personal property tax is paid by any person.

Thus, Claude owns a store. Every year, he pays corporate tax. Option B is correct.

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Using substitution method, the solution of the equations are x = 1 and y = 9.

The system of equation can be solved using substitution method as follows:

9x + y = 18

4x - 2y = -14

Let's make y the subject of the formula in equation(i)

9x + y = 18

y = 18 - 9x

Substitute the value of y in equation(ii)

4x - 2y = -14

4x - 2(18 - 9x) = -14

4x - 36 + 18x = - 14

4x + 18x  = -14 + 36

22x = 22

divide both sides by 22

x = 22 / 22

x = 1

Let's find the value of x using equation(i)

y = 18 - 9x

y = 18 - 9(1)

y = 18 - 9

y = 9

Therefore, x = 1 and y = 9.

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Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.

The total monthly salary of Mr. Mensah is 4500.

He is required to pay 5.5% of his salary into a social security fund.

Now, we have to find the amount he has to pay each month into the social security fund.

To find that, we need to find the value of 5.5 percent of 4500.

4500 ×5.5/100

45×5.5

247.5

Therefore, 5.5% of 4500 is 247.5.

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Answer:

1. x = 62.7 , y = 12.4

2. x = 5.9 , y = 19.2

Step-by-step explanation:

sorry i dont have the time to explain...

Answer:

Obtuse Triangle

Step-by-step explanation:

An obtuse triangle has one angle greater than 90 degrees.

Given the Trigonometric Functions:

Using your calculator you get:

By definition, Secant is negative in Quadrant III.

Finds its Reference Angle as follows:

Because:

Then, you get:

Notice that:

Then, you can conclude that it is in Quadrant II.

Therefore its Reference Angle is:

So you can set up:

By definition:

Therefore, you can rewrite it in this form:

Hence, the answer is:

Answer:

4√3/3

Step-by-step explanation:

Find the diagram attached below

Considering angle 60°

Opposite side = 2

Hypotenuse = x

Using the SOH CAH TOA identity

sin theta  = opposite/hypotenuse

sin 60 = 2/x

x = 2/sin60

x = 2/(√3/2)

x = 2 * 2/√3

x = 4/√3

Rationalize

x = 4/√3 * √3/√3

x = 4√3/3

Hence the value of x in its simplest form is x = 4√3/3

Answer: C. t < -3

Hope this helps!

Answer: C. t < -3

Because i made a 100 on my test