Is the cost of candy proportional to pounds of candy?

In Euler's Formula for graphs that are not necessarily connected states that the number of vertices minus the number of edges plus the number of connected components is equal to the Euler characteristic of the graph.

Euler's Formula, which states that the number of vertices minus the number of edges plus the number of faces is equal to 2 for planar graphs, can be extended to graphs that are not necessarily connected. In this generalization, we consider the number of connected components in the graph. A connected component is a subgraph where there is a path between any two vertices.

Let V be the number of vertices, E be the number of edges, C be the number of connected components, and X be the Euler characteristic of the graph. The generalization of Euler's Formula for non-connected graphs is given by V - E + C = X.

To prove this formula, we start with Euler's Formula for connected graphs, which states V - E + F = 2, where F is the number of faces. For a disconnected graph, the number of faces can be defined as the sum of the number of faces in each connected component minus the number of edges that belong to more than one connected component. This can be written as F = F1 + F2 + ... + FC - N, where Fi is the number of faces in the i-th connected component and N is the number of edges connecting different components.

By substituting F = F1 + F2 + ... + FC - N into Euler's Formula for connected graphs and rearranging terms, we get V - E + C = X, which is the generalization of Euler's Formula for non-connected graphs. Therefore, the formula holds true for any graph, whether connected or not.

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Answer:

The population of the town in Iowa after 13 years is 9,130

Step-by-step explanation:

The given parameters of the town are;

The population of the town in Iowa in 2007, a = 12,355

The rate at which the people of the town leave Iowa for Minnesota, r = 2.3% per year

We are required to find the population of the town after t = 13 years

The given population decay function is presented as follows;

[tex]f(t) = a \cdot (1 - r)^t[/tex]

Where;

a = The initial population of the town = 12,355

r = The annual percentage rate at which the people of the town leave Iowa for Minnesota = 2.3% per year = 0.023

t = The number of years over which the population changes = 13 years = 13

∴ f(13) = 12,355 × (1 - 0.023)¹³ = 9130.02734094

Therefore, the population of the town in Iowa after 13 years ≈ 9,130 (we round down to the nearest whole number).

Answer:

50 x 100=5,000

Step-by-step explanation:

50 x 100

Answer:

The equation is x-18 + 8x = 180 (because they form a linear pair of angles.

Each angle measure:-

x-18 + 8x = 180

x + 8x = 180 + 18 (-18 becomes +18)

9x = 198

x = 198/9

x = 22

Angle 1 = x-18 = 22-18 = 4 degrees

Angle 2 = 8x = 8 * 22 = 176 degrees

Hope it helps :')

Answer:

Answer is A.  -296x+960/ -636x+3,024

Step-by-step explanation:

Answer:

HEREEE besties

Answer:

d) population is divided into similar groups and a SRS is chosen from each group.

Step-by-step explanation:

Stratified random sampling

can be regarded as "proportional random sampling" and is method of sampling which entails division of a population to more simpler sub- groups, this sub- groups are regarded as " strata". This strata are been formed on the basis of shared attributes of the members. This attribute could be educational attainment as well as income. It should be noted that stratified random sample is population is divided into similar groups and a SRS is chosen from each group.

Answer:

The 6th term of the sequence is 6144/243

Step-by-step explanation:

From what we have, we can see that the sequence might be geometric

to confirm this, we have to check if the common ratio is the same all through

To know this, we have to divide the succeeding term by the preceding term and check if the results for two sets are equal

thus, we have it that;

32/3 * 1/8 = 8/6

= 4/3 = 4/3

We can confirm that the sequence is thus geometric

Now, to find the nth term of a geometric sequence, we have it that;

Tn = ar^(n-1)

where a is the first term, given as 6

r is the common ratio given as 4/3

n is the term number given as 6

Thus, we have this as:

T6 = 6 * (4/3)^(6-1)

T6 = 6 * (4/3)^5

T6 = 6144/243

Answer:

$4.20 / box

Step-by-step explanation:

12.60 / 3 = 4.20

Both (4, 1) and (5, 2) is the solution to the given equation. Therefore, option C is the correct answer.

The given equation is y+1=3(x-4).

A) The given coordinate point is (4, -1).

Substitute (x, y)=(4, -1) in y+1=3(x-4), we get

-1+1=3(4-4)

0=0

So, (4, -1) is the solution to the given equation.

B) The given coordinate point is (5, 2).

Substitute (x, y)=(5, 2) in y+1=3(x-4), we get

2+1=3(5-4)

3=3

So, (5, 2) is the solution to the given equation.

C) Here, both (4, 1) and (5, 2) is the solution to the given equation.

Therefore, option C is the correct answer.

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The general solution to the differential equation is: y = -(3/2)x + C, where C is the constant of integration.

To solve the differential equation 6x dx + 4x dy = 0 using separation of variables, we need to rearrange the equation so that all the x terms are on one side and all the y terms are on the other side.

Let's start by dividing both sides of the equation by 4x:

(6x dx + 4x dy) / 4x = 0

(6x / 4x) dx + (4x / 4x) dy = 0

(3/2) dx + dy = 0

Now we can separate the variables by moving the dy term to the other side:

dy = -(3/2) dx

Integrating both sides with respect to their respective variables, we have:

∫ dy = ∫ -(3/2) dx

The integral of dy with respect to y is simply y, and the integral of -(3/2) dx with respect to x is -(3/2)x:

y = -(3/2)x + C

where C is the constant of integration. Thus, the general solution to the differential equation is:

y = -(3/2)x + C

This is the final solution using separation of variables.

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Answer:

Step-by-step explanation:

This is a quartic  equation with a positive coefficient for x^4 so it is shaped like an M xo ir rises to both the left and the right.

Answer:

I need help with math too. Can u help me and I’ll help u

Step-by-step explanation:

a.  The 68% of the widget weights lie between  33 ounces and  55 ounces.

b. The percentage of widget weights lying between 11 and 55 ounces is approximately 68%.

c. The percentage of widget weights lying above 22 ounces is approximately = 5%.

Based on the given data points: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, the five-number summary can be identified as follows:

Minimum: 5

First Quartile (Q1): 7

Median (Q2): 11

Third Quartile (Q3): 15

Maximum: 18

Now, let's answer the questions related to the distribution of widget weights using the Empirical Rule:

a) The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data lies within one standard deviation of the mean. Since the mean is 44 ounces and the standard deviation is 11 ounces, we can say that approximately 68% of the widget weights lie between 44 - 11 = 33 ounces and 44 + 11 = 55 ounces.

b) To determine the percentage of widget weights lying between 11 and 55 ounces, we need to calculate the z-scores for these values. The z-score is calculated using the formula: z = (x - mean) / standard deviation.

For 11 ounces: z1 = (11 - 44) / 11 = -33/11 = -3

For 55 ounces: z2 = (55 - 44) / 11 = 11/11 = 1

Using the Empirical Rule, we know that approximately 68% of the data lies within one standard deviation of the mean. Therefore, the percentage of widget weights lying between 11 and 55 ounces is approximately 68%.

c) To determine the percentage of widget weights lying above 22 ounces, we need to calculate the z-score for 22 ounces: z = (22 - 44) / 11 = -22/11 = -2.

Using the Empirical Rule, we know that approximately 95% of the data lies within two standard deviations of the mean. Therefore, the percentage of widget weights lying above 22 ounces is approximately 100% - 95% = 5%.

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Answer:

46.08

Step-by-step explanation:

you have to make your percentage a decimal, which 60% will be .60 and 20% will be .20. you then multiply your initial number which is 36 by .60 and add that on because youre adding 60%. After that you will multiply that given number by .20 and you subtract what that product is from your last product you received (36x.60) which if im not mistaken will give you $46.08.

Answer:

C

Step-by-step explanation:

I took the test

Answer:

equal

Step-by-step explanation:

Most quadratic equations have equal roots.

13. k=3/4       14. a=23

15. p= 5 1/2    16. x=13

17. m=56         18. n=1 1/2

Answer:

13)

14)

15)

16)

17)

18)

Answer:

The height of the kite from the ground is 13.617 feet  

Step-by-step explanation:

Given as :

The measure of the string = 30 feet

The angle of elevation from the boy to his kite = 27°

Let the height of the kite from ground = H feet

So, From Triangle

Sin angle =

Or, Sin 27° =  

or, H = 30 ×  Sin 27°

I.e H = 30 × 0.4539

∴ H = 13.617 feet

Hence the height of the kite from the ground is 13.617 feet   Answer

The lifetimes of a certain brand of photographic light are normally distributed with a mean of 210 hours and a standard deviation of 50 hours. We need to find the probability that a particular light will last more than 250 hours.

Given mean = μ = 210 hours. Standard deviation = σ = 50 hours. Let X be the lifetime of a photographic light. X ~ N (μ, σ) = N (210, 50). The probability that a particular light will last more than 250 hours can be calculated as follows: P(X > 250) = 1 - P(X < 250)Let Z be the standard normal variable.

Then, (250 - μ) / σ = (250 - 210) / 50 = 0.8P(X < 250) = P(Z < 0.8). Using the z-table, the probability that Z is less than 0.8 is 0.7881. Therefore, P(X > 250) = 1 - P(X < 250) = 1 - 0.7881 = 0.2119. Hence, the probability that a particular light will last more than 250 hours is 0.2119.

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Answer:

1 hour

Step-by-step explanation:

Travels 18 km/h

km/h = kilometers per hour

Answer:

1 hour

Step-by-step explanation:

The volume, in cubic inches, of the cylinder will be   [tex]\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches.

Cylinder is a [tex]3D[/tex] solid shape which holds two parallel bases joined by a curved surface, at a fixed distance. These bases are circular in shape and the center of the two bases are joined by a line segment.

Volume is define as capacity of cylinder.

Volume of cylinder [tex]=\pi r^{2} h[/tex]

We have,

Radius [tex]=3[/tex] inches

Height [tex]=5[/tex] inches,

Then,

Volume of cylinder [tex]=\pi r^{2} h[/tex]

                              [tex]=\frac{22}{7} *(3)^{2} *5[/tex]

                               [tex]=\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches

Hence, we can say that The volume, in cubic inches, of the cylinder will be     [tex]\frac{990}{7}[/tex]  or [tex]45\pi[/tex] cubic inches

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Statistic 1 would you recommend for estimating average of smallest and largest values in the sample

To compute Statistics 1, 2, and 3 for the given samples, and determine which statistic would be recommended for estimating the average of the smallest and largest values, let's go through each sample one by one:

1. 2,3,3*

 Statistics 1: Sum of the values = 2 + 3 + 3 = 8

 Statistics 2: Average of the values = (2 + 3 + 3) / 3 = 2.67

 Statistics 3: Median of the values = 3

2. 2,3,4

   Statistics 1: Sum of the values = 2 + 3 + 4 = 9

   Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

   Statistics 3: Median of the values = 3

3.  2,3,4*

    Statistics 1: Sum of the values = 2 + 3 + 4 = 9

    Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

    Statistics 3: Median of the values = 3

4. 2,3*,4*

Statistics 1: Sum of the values = 2 + 3 + 4 = 9

Statistics 2: Average of the values = (2 + 3 + 4) / 3 = 3

Statistics 3: Median of the values = 3

5. 2,4,4*

Statistics 1: Sum of the values = 2 + 4 + 4 = 10

Statistics 2: Average of the values = (2 + 4 + 4) / 3 = 3.33

Statistics 3: Median of the values = 4

6. 3,3*,4

Statistics 1: Sum of the values = 3 + 3 + 4 = 10

Statistics 2: Average of the values = (3 + 3 + 4) / 3 = 3.33

Statistics 3: Median of the values = 3

7.  3,3*,4*

Statistics 1: Sum of the values = 3 + 3 + 4 = 10

Statistics 2: Average of the values = (3 + 3 + 4) / 3 = 3.33

Statistics 3: Median of the values = 3

8.  3,4,4*

Statistics 1: Sum of the values = 3 + 4 + 4 = 11

Statistics 2: Average of the values = (3 + 4 + 4) / 3 = 3.67

Statistics 3: Median of the values = 4

9.  3*,4,4*

Statistics 1: Sum of the values = 3 + 4 + 4 = 11

Statistics 2: Average of the values = (3 + 4 + 4) / 3 = 3.67

Statistics 3: Median of the values = 4

For estimating the average of the smallest and largest values in the sample, the recommended statistic would be Statistics 1, which is the sum of the values. Taking the average of the smallest and largest values can be obtained by dividing the sum by the number of values, which in this case is 3.

Therefore, the recommended statistic for estimating the average of the smallest and largest values is Statistics 1 (sum of the values).

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The 90% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is -21.3% to -16.1%, which represents the range of values within which the true difference is likely to fall.

To construct the confidence interval, we first calculate the sample proportions for Democrats and Republicans: p₁ = 644/700 ≈ 0.92 for Democrats, and p₂ = 323/850 ≈ 0.38 for Republicans.

Next, we calculate the standard error of the difference using the formula: SE = √((p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂)), where n₁ and n₂ are the sample sizes.

Using the given sample sizes, the standard error is approximately 0.019.

To determine the margin of error, we multiply the standard error by the z-score corresponding to a 90% confidence level, which is approximately 1.645.

Finally, we calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error from the difference in sample proportions: 0.92 - 0.38 ± (1.645 * 0.019).

The resulting confidence interval is approximately -21.3% to -16.1%, which represents the range within which we can estimate the overall difference in the percentages of Democrats and Republicans prioritizing environmental protection.

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The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

To calculate the income elasticity of demand, we need to use the formula:

Income Elasticity of Demand = Percentage change in quantity demanded / Percentage change in income

Given that incomes increase by 58% and the quantity demanded of tennis balls drops by 87%, we can plug these values into the formula:

Income Elasticity of Demand = (-87%)/58%

Simplifying the calculation:

Income Elasticity of Demand = -1.5

The income elasticity of demand for tennis balls is -1.5. The negative sign indicates an inverse relationship between income and the quantity demanded of tennis balls, suggesting that tennis balls are an inferior good.

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Answer:

he needs to play 24 games of basketball

Answer:

A = 1413.72 unit²

Step-by-step explanation:

area of a semicircle formula: A = (πr²)/2

To find the area of a semicircle that has a radius of 30 feet, apply r = 30 to the formula A = (πr²)/2:

A = (π30²)/2

A = 1413.72 unit²

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Answer:

740%

Step-by-step explanation:

The specificity of the diagnostic test is 88%, indicating its ability to accurately identify individuals without the disease as negative.

Specificity is a measure of the test's ability to correctly identify individuals without the disease as negative. To calculate the specificity, we need to consider the number of true negatives (controls who yield negative tests) and the total number of controls.

In this case, the number of controls tested is 250, and out of those, 30 yield positive tests. The number of true negatives can be calculated by subtracting the number of false positives (controls who yield positive tests) from the total number of controls:

Negatives which are true = Total Controls - False Positives

True Negatives = 250 - 30 = 220

The specificity is then calculated as the ratio of true negatives to the total number of controls:

Specificity = True Negatives / Total Controls

Specificity = 220 / 250 ≈ 0.88

Therefore, the specificity of this test is approximately 0.88 or 88%. This means that the test correctly identifies 88% of individuals without the disease as negative.

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Answer:

381 in^3

Step-by-step explanation:

The volume of the green block is V1 = length(width)(height), or

                                                         V1 = (16 in)(7 in)(3 in) = 336 in^3, and

the volume of the red triangular prism is V2 = (1/2)(3 in)(5 in)(6 in) =

                                                           V2 = 45 in^3

So the total volume is the sum of these two results:  381 in^3

Answer: $50 withdrawl $50 withdrawl and $65 deposite

Step-by-step : $50 withdrawl $50 withdrawl and $65 deposite