Suppose there is a shipping network with n shipping locations, where n ≥ 2. They are connected by roads, but a shipping location could be isolated (i.e. there are no roads to it). Prove that, no matter how these roads are organized, there are at least two shipping locations with the same number of roads

Answer:

Negative

Step-by-step explanation:

If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3

Two expressions with equal sign is called as Equation. The rating of a brand that costs $3.00 per bag is 7.

Two expressions with equal sign is called as Equation.

A simple linear regression equation is used to estimate the value of the dependent variable based upon the independent variable.

The general form of a simple linear regression equation is:

y=a+bx

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The output of the least squares regression analysis for predicting rating from price is provided.

So, the dependent variable is the ratings and the independent variable is the price.

The regression equation for predicting rating from price is:

y=0.39+2.52x

Predict the rating of a brand that costs $3.00 per bag as follows:

y=0.39+(2.52*$3.00)

=0.39+7.56

=7.17

=7 approximately.

Thus, the rating of a brand that costs $3.00 per bag is 7.

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Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as \(X^c\)∩\(Y^c\)∩\(Z^c\)

By set theory, we have;

\(\left | X^c \cap Y^c \cap Z^c \right |\) = \(\left | X^c \cup Y^c \cup Z^c \right |\) =  \(\left | U \right | - \left | X \cup Y \cup Z \right |\)

\(\left | U \right | - \left | X \cup Y \cup Z \right |\) = \(\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)\)

Therefore;

\(\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)\)

Where;

\(\left | U\right |\) = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

\(\left | X\right |\) = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

\(\left | Y\right |\) = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

\(\left | Z\right |\) = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

\(\left | X \cap Y\right |\) = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | X \cap Z\right |\) = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | Y \cap Z\right |\) = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | X \cap Y \cap Z\right |\) = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

\(\left | X^c \cap Y^c \cap Z^c \right |\) = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

\(\left | X^c \cap Y^c \cap Z^c \right |\) = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as \(\left | X^c \cap Y^c \cap Z^c \right |\)  = 1,968

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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If a cylinder has a volume of 600 cubic inches, and we want to find the volume of a cone with the same diameter and height as the cylinder, we can use the formula for the volume of a cone.

The formula for the volume of a cone is given as:

\(V = (1/3) * \pi * r^2 * h,\)

where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cone, and h is the height of the cone.

In this case, since the cylinder and cone have the same diameter, the radius of the cone's base will be half of the radius of the cylinder's base. Let's assume the radius of the cylinder's base is r_cylinder.

So, the radius of the cone's base will be r_cone = r_cylinder / 2.

The height of the cone will be the same as the height of the cylinder, denoted as h_cylinder.

Now, let's substitute these values into the volume formula for the cone:

V_cone = (1/3) * π * (r_cone)^2 * h_cylinder

      = (1/3) * π * (r_cylinder/2)^2 * h_cylinder

      = (1/3) * π * (r_cylinder^2 / 4) * h_cylinder

      = (π/12) * r_cylinder^2 * h_cylinder.

Since we know the volume of the cylinder is 600 cubic inches, which is equal to the volume of the cone, we have:

600 = (π/12) * r_cylinder^2 * h_cylinder.

From this equation, we can't directly calculate the specific values of r_cylinder and h_cylinder. We would need additional information or constraints to solve for them.

However, using the given information, we can conclude that the volume of the cone with the same diameter and height as the cylinder will also be 600 cubic inches, assuming the cylinder and cone share the same dimensions.

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Answer: 6

Step-by-step explanation: .

Answer:

x=12.92

cube root of 9 Is 2.08 so you minus 15-2.08=12.92

In the four levels of measurement : nominal,  interval, ordinal, ratio: "ordinal," is most appropriate for the given for positions of the persons standing in a line

Four degrees of measuring exist:

Thus, in the four levels of measurement : nominal,  interval, ordinal, ratio: "ordinal," is most appropriate.

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The complete question is-

determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for positions of persons in a line (extra?)

Answer:

Slope is -2

Step-by-step explanation:

Answer:

x = 73

Step-by-step explanation:

The measure of the sum of the arcs in a circle = 360°.

Sum the given arc measures and equate to 360, that is

95 + 52 + 67 + 2x = 360

214 + 2x = 360 ( subtract 214 from both sides )

2x = 146 ( divide both sides by 2 )

x = 73

Answer:

-1

Step-by-step explanation:

Answer:

• Factorization identity

\({ \tt{24x + 34y}} \\ = { \boxed{ \tt{ \: 2(12x + 17y)}}}\)

Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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Answer: 40% of the fruit pieces are apples

Step-by-step explanation:

\(\frac{6}{15}\) = .4

.4 x 100% = 40%

Answer:

y=5.5x+100

Step-by-step explanation:

since the $5.50 is your variable, you set that to the x value, and 100 to reserve is your y intercept because it is constant.

According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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This situation does not contradict Rolle's Theorem because Rolle's Theorem requires the function to be continuous on a closed interval and differentiable on an open interval, which is not satisfied by f(x) = tan x in the interval (0, π).

To show that f(0) = f(π), we evaluate the tangent function at these points. At x = 0, tan(0) = 0, and at x = π, tan(π) = 0. Therefore, f(0) = f(π).

To investigate whether there exists a number c in the interval (0, π) such that f'(c) = 0, we need to find the derivative of f(x). The derivative of tan x is given by f'(x) = sec² x. However, the secant squared function is never equal to zero. Therefore, there is no c in the interval (0, π) where f'(c) = 0.

This situation does not contradict Rolle's Theorem because Rolle's Theorem requires certain conditions to be met. First, the function must be continuous on the closed interval [a, b], which is not satisfied by f(x) = tan x since it is not defined at x = π/2. Second, the function must be differentiable on the open interval (a, b), but f'(x) = sec^2 x is not defined at x = π/2. Thus, the requirements of Rolle's Theorem are not fulfilled, and its conclusion does not apply to f(x) = tan x in the interval (0, π).

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The type of nonprobability design that is most likely to yield a representative sample is a stratified random sampling.

In stratified random sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables that are relevant to the research objective. Then, a random sample is selected from each stratum proportionally to the size or importance of that stratum in the population. This approach ensures that the sample reflects the diversity and heterogeneity of the population.

By stratifying the population and using random sampling within each stratum, the stratified random sampling design increases the likelihood of obtaining a representative sample. It allows for accurate representation of different groups within the population, which can help reduce sampling bias and provide more precise estimates of population characteristics.

However, it's important to note that even with stratified random sampling, there may still be limitations and potential sources of bias. Factors such as nonresponse rates and the accuracy of the population data used for stratification can impact the representativeness of the sample. Nevertheless, when properly implemented, stratified random sampling is a valuable nonprobability design for achieving representativeness in a sample.

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The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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The standard deviation is 8.

Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high. A measure of a group of values' variance or dispersion in statistics is called the standard deviation. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high. The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

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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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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

b = 4.66666667

Step-by-step explanation:

The equation for finding the area of a triangle is

0.5b x h = a

b = base

h = height

a = area

So I calculated 14 divided by 6

And got 2.3333333

And since that number is half of the base, I multiplied it by 2

2.333 x 2 ≈ 4.66666667

Answer:

3.3

Step-by-step explanation:

my dad is helping me just simplify

Answer:

a 90

b 90

a 8x+40

b 4y-36

c -6n-3

d 7x+7

e -10x+30

f 4/1x+2/1

Answer: 180

Step-by-step explanation:

1) Add the two angles together

160 + 20 = 180

180

You can tell this because a 180-degree line is flat, just like in this picture.

The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

The given table shows the height of a candle as it burns continuously over time. The first column represents time in hours, ranging from 0 to 1, while the second column represents the corresponding height in centimeters.

From the data, we can observe that the candle starts at a height of 25 centimeters when the time is 0 hours. As time progresses, the height of the candle decreases gradually. Specifically, for every hour that passes, the candle burns 0.625 centimeters.

Therefore, the main answer is that the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

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Answer:

C

Step-by-step explanation:

Line of symmetry

Answer:

After 4 movies it will be equal

Step-by-step explanation:

10x + 160 = 50x

160 = 40x

4 = x

Check:

10x + 160 =

10(4) + 160 =

40 + 160 = 200

50x =

50 x 4 = 200

200 = 200