Number 13 and 14 don’t matter but help ‼️

The following are the statements which are true to the following:

a. simple graph does not have parallel edges or self-loops.

b.  in a connected, directed graph, every node is reachable from all other nodes.

c.  there cannot be any cycle in a tree.

d.  if a graph g is a forest, then there is no cycle in g.

We have the following:

a. a simple graph devoid of self-loops or parallel edges. consequently valid.

A simple graph is one that doesn't contain self-loops or parallel edges.

b. In a directed, connected graph, every node may be reached from every other node. consequently valid.

When all of the directed edges in a directed graph are replaced with undirected edges, the resulting undirected underlying graph is a connected graph, which indicates that the directed graph is weakly connected (or just connected).

c. A tree cannot contain a cycle. consequently valid

The aforementioned claim is accurate. Cycles cannot be contained in a tree since it is a non-linear data structure. Cycles are a possible feature of a graph.

d. If a graph g is a forest, then g does not include a cycle. consequently valid

The acyclic graph of a forest (i.e., a graph without any graph cycles). Therefore, forests are made up only of (potentially unconnected) trees, therefore the name "forest." All trees, empty graphs, and the singleton graph are a few examples of forests.

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Answer:

the correct graph is the one that shows a horizontal segment, followed by a positive slope segment, followed by a flat segment, and then a negative slope segment that is option B.

What is graph?

In mathematics, a graph is a visual representation of a set of objects and the connections between them. The objects, which are often called vertices or nodes, are typically represented by points or circles on the graph. The connections between the objects, which are often called edges or arcs, are typically represented by lines or curves connecting the points or circles.

Here,

To represent Marie's situation in a graph, we need to plot her golf cart's distance from the first hole over time. Let's analyze the given information to determine what the graph should look like.

For the first 30 minutes, Marie stayed at the first hole, so her distance from the first hole would be 0 during that time.

For the next 2 hours, Marie drove away from the first hole. Her distance from the first hole would increase during this time.

After 2 hours of driving, Marie stopped for lunch. Her distance from the first hole would remain constant during this time.

After lunch, Marie took 2 more hours to drive back to the first hole. Her distance from the first hole would decrease during this time.

The x-axis represents time in hours, and the y-axis represents distance from the first hole in miles. The graph starts at the origin, where the golf cart stays for the first 30 minutes, and then goes up with a positive slope for 2 hours as the golf cart moves away from the first hole. Then, the graph remains flat for 1 hour during lunch, before going down with a negative slope for 2 hours as the golf cart returns to the first hole.

As a result, the right graph is option B, which displays a horizontal section followed by a positive slope segment, a flat segment, and then a negative slope segment.

Step-by-step explanation:

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

A. EF

Step-by-step explanation:

Answer:

EF

Step-by-step explanation:

The reason is because EF and BC are in the same plane

\(3 \sqrt{13} \)

Answer:

E = 7.30 J

PE = 7.30 J

KE = 0

Step-by-step explanation:

Given;

maximum height, h = 1.2 m

mass of the object, m = 0.62 kg

velocity, v = 0 m/s

acceleration due to gravity, g = 9.81 m/s²

To determine;

The potential energy, PE = mgh

                                    PE = 0.62 x 9.81 x 1.2

                                    PE = 7.30 J

The kinetic energy, KE = ¹/₂mv²

                                KE = ¹/₂ x 0.62 x 0

                               KE = 0

The total mechanical energy, E = PE + KE

                                                 E = 7.30 J + 0

                                                E = 7.30 J

Answer:

x > 1

Step-by-step explanation:

Subtract 3 from both sides

8x + 3 - 3 > x + 10 - 3

Simplify

8x > x + 7

Subtract x from both sides

8x - x > x + 7 - x

Simplify

7x - 7

Divide both sides by 7

7x/7 > 7/7

Simplify

x > 1

Answer:

Explanation below

Step-by-step explanation:

Angles in a Triangle

There are two basic relations of angles we need to recall:

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

a + b = d

Answer:The solution is in the file below

Step-by-step explanation:

Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3

Step-by-step explanation:

The range of the men's scores is 75-65 (highest-lowest), which is 10.

The range of the woman's scores is 80-69, which is 11.

The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.

Men's MAD:
The mean is \(\frac{65+68+70+72+73+75}{6}\), which is 70.5.

Sigh.

Now, we find the difference of each term to the mean.

\(70.5-65= 5.5\)

\(70.5-68=2.5\)

\(70.5 - 70 = 0.5\)

\(72-70.5=1.5\)

\(73-70.5=2.5\)

\(75-70.5=4.5\)

wow. Now, we find the mean of these numbers.

\(\frac{5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5}{6}\)= 17/6=2.8333333333 This is the MAD.

For the Women's, I'll speed over it.

The mean is 74.

The MAD is 3.

The dropping degree temperature will be  -12°.

A drop of 17 degrees means subtract 17  from given temperature

∴5°-17°=-12°

so, the Temperature drop will be -12°

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Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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Answer:

The price of the car is $12,000. The individual makes a down payment of 25%, so the loan amount is $9,000. The interest rate is 8% compounded monthly, so the monthly interest rate is 0.08/12 = 0.00667. The loan term is 48 months, so the number of payments is 48.

The monthly payment is calculated using the following formula:

Monthly payment = Loan amount * (Monthly interest rate) / (1 - (1 + Monthly interest rate) ^ (-Number of payments))

Monthly payment = $9,000 * (0.00667) / (1 - (1 + 0.00667) ^ (-48))

Monthly payment = $219.72

The total interest charges are calculated using the following formula:

Total interest charges = Total payments - Loan amount

Total interest charges = 48 * $219.72 - $9,000

Total interest charges = $1,510.72

Therefore, the correct answer is: c. R= $219.72; interest charges= $1,510.72.

Step-by-step explanation:

Answer:

The factors of 27 are 1,3,9,27.

The factors of 36 are 1,2,3,4,6,9,12,36.

HCF=1,3,9

we can factor the whole thing:

(2sin(x) -1)(sin(x)+1) = 0.

Therefore, sin(x) = -1 and sin(x) = 1/2.

For the first one x = 3π/2 and the second is π/6 and 5π/6

So 3π/2, π/6 and 5π/6 are the solutions.

I do kind of have a problem with this because it doesn't mention if you should go over 360°. Otherwise, you have to add in an 2nπ into the equations like 3π/2 + 2nπ; \(n \in \mathbb{W}\)

but I don't know if that is necessary for you.

Answer:

0.000000207 in scientific notation = 2.07 × 10^-7

Remember it has to have one number before the decimal.

8.2 * 10^-7 in standard form = 0.00000082

YOu have to move the decimal back.

In the first box the answer is 2.07 × 10^-7.

In the second box the answer is 0.00000082.

Answer:

sorry for the messy handwriting- hope this helps

Step-by-step explanation:

Answer:

4 x 4 = 16

5 x 12 = 60

_________+

76

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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Answer: 6 hours

Step-by-step explanation:

48/6 = 8

36/6 = 6

SOLUTION

(c) The values of x for which f(x) = -1

Looking from the graph, this does not exist.

Hence the answer is "None"

(d) The values of x for which f(x) = -3

Looking form the graph, this is between 0 and 1

So we have this as

So in interval notation, the answer is

(e) The x-intercept is where the graph cuts the x-axis

The graph cuts the x-axis at -1

Hence the answer is (-1, 0)

Answer: imaginary axis

Step-by-step explanation:

Answer:

draw 3cm lines each sides and you get the rectangle

Step-by-step explanation:

it's 3cm because a rectangle has 4 side when you divide 12cm by 4cm you get 3cm

Answer: answer is 12

Step-by-step explanation:

The height of the building, to the nearest foot, is approximately 120 feet. This is calculated using the tangent function with the angle of 57° and the distance of 78 feet from the woman to the base of the building.

To solve this problem, we can use trigonometry and the tangent function to find the height of the building. Let's denote the height of the building as h.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the woman to the base of the building (78 ft).

Therefore, we have the equation:

tan(57°) = h/78

To solve for h, we can multiply both sides of the equation by 78:

78 * tan(57°) = h

Using a calculator, we can evaluate the right-hand side of the equation:

78 * tan(57°) ≈ 120.416

Therefore, the height of the building, to the nearest foot, is approximately 120 feet.

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The simplified expression is 2y² - 9.

To subtract the binomials (-3y^2 - 8) - (-5y^2 + 1), we need to distribute the negative sign to the terms inside the second set of parentheses:

(-3y^2 - 8) - (-5y^2 + 1) = -3y^2 - 8 + 5y^2 - 1

Next, we combine like terms by adding or subtracting the coefficients of the same degree:

-3y^2 + 5y^2 - 8 - 1 = (5y^2 - 3y^2) + (-8 - 1) = 2y^2 - 9

Therefore, the simplified expression is 2y² - 9.

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By applying the fraction concept, we can conclude that the bunny ate 3/10 food at night.

Application of the concept of fractions in real life

In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.

In the problem above it is stated that initially the bunny has food, which will be eaten in the morning and at night, and some food was left over.

If x is the total food for the bunny, then the given problem can be written mathematically as follows:

breakfast (a) : a = 1/2x

dinner (b)

food left (c) : c = 1/5x

Then the mathematical expression that describes the above situation is as follows:

x = a + b + c

  = 1/2x + b + 1/5x --> then we make the denominators the same, so it becomes:

           x = 5/10x + b + 2/10x

              = 7/10x + b

x - 7/10x = b

     3/10x = b

So, the food that the bunny eats at night was 3/10.

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Answer:

So, the food that the bunny eats at night was 3/10.

:D im jus smart.

Answer:

equaloty

Step-by-step explanation:

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Answer:

x+4/5x

Step-by-step explanation:

x is increased by 80% 0f it self

80%of x= 4/5x

... x+4/5x

Answer:

$100 (rounding)

Step-by-step explanation:

Morning

in- 8 am

out- 12 pm

hours worked= 12-8

                       = 4hrs

After-noon

In- 12:45 pm

Out- 17:30 pm

hours worked= 4hrs 45min

Total working time= 8hrs 45 mins

$11 per hour

So, 8hrs wage= 11*8

                        =$88

60 min- $11

1 min  - 11/60

45 min- (11*45)60

           =$8.25

Total, wage= $(88+8.25)

                   =$ 96.25