a connected planar graph has 9 vertices having degrees 2, 2, 2, 3, 3, 3, 4, 4, and 5. how many edges are there? how many faces are there?

There seems to be an error in the problem statement or some information is missing.

Let's represent the amount of juice the pitcher holds when it's full by x.

According to the problem, the pitcher is initially half empty, which means it is filled with x/2 amount of juice.

After 1/2 cup of juice is added, the pitcher becomes full, which means it is now filled with x amount of juice.

So, the amount of juice added to the pitcher is (x - x/2) + 1/2 = x/2 + 1/2.

Since this amount is equal to 1/2, we can write the equation:

x/2 + 1/2 = 1/2

Solving for x, we get:

x/2 = 0

Multiplying both sides by 2, we get:

x = 0

This means that the pitcher does not hold any juice when it's full, which is not a valid answer.

Learn more about statement here

https://brainly.com/question/28936505

#SPJ11

Answer:

Step-by-step explanation:

The equation is y=7x

x      y          Calculation

5     35         y=7x, y=7*5, y=35

6     42         y=7x, y=7*6, y=42

7      49       y=7x, y=7*7, y=49

8     56          y=7x, y=7*8, y=56

The values of T(0) = e(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), r''(t) = 8e^(2t) + 8e^(-2t).

We are given that r(t) = e^(2t), e^(-2t), te^(2t). To find T(0), we need to evaluate the unit tangent vector T(t) at t=0. The formula for the unit tangent vector is T(t) = r'(t)/|r'(t)|, where |r'(t)| is the magnitude of r'(t).

r'(t) = 2e^(2t) - 2e^(-2t), so r'(0) = 2 - 2 = 0.

Thus, T(0) = r'(0)/|r'(0)| = 0/|0|, which is undefined.

However, since r'(0) = 0, we can use the normal vector instead to find the direction of the tangent line at t=0.

The normal vector N(0) is given by N(t) = T'(t)/|T'(t)|. To find T'(t), we differentiate r'(t) with respect to t:

r''(t) = 4e^(2t) + 4e^(-2t)

So, r''(0) = 4 + 4 = 8. Thus, T'(0) = r''(0)/|r'(0)| = 8/0, which is undefined.

To find r'(t), we can differentiate r(t) using the product rule:

r'(t) = 2e^(2t), -2e^(-2t), 2te^(2t) + e^(2t)

To find r''(t), we can differentiate r'(t):

r''(t) = 4e^(2t), 4e^(-2t), 4te^(2t) + 4e^(2t)

Thus, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

Therefore, T(0) = e^(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

To learn more about tangent vector, click here: brainly.com/question/30550139

#SPJ11

To compare the likelihoods of two candidates winning their elections when they are running in different elections, it is important to collect relevant data such as historical voting patterns, demographic information, campaign funding, candidate popularity, and election-specific factors.

1. This data will allow for a comprehensive analysis that considers various factors influencing the outcomes of elections and enables a fair comparison between the candidates.

2. When comparing the likelihoods of two candidates winning their elections in different contexts, several types of data should be collected and analyzed. Firstly, historical voting patterns and trends in the respective regions where the elections are taking place are essential. This data can provide insights into the voting behavior of the electorate and help identify any consistent patterns or shifts in support for particular candidates or parties.

3. Demographic information is another crucial factor. Understanding the composition of the electorate in terms of age, gender, ethnicity, socioeconomic status, and other relevant factors can provide valuable insights into the candidate's potential support base and help gauge the likelihood of their success.

4. Campaign funding is an important indicator of a candidate's resources and support. Analyzing the financial contributions and expenditures of each candidate can provide insights into their campaign strategies, level of organization, and potential impact on the electorate.

5. Candidate popularity and public opinion data are also crucial. Collecting and analyzing polling data, surveys, and public sentiment from reputable sources can help assess the candidates' popularity, public perception, and the overall sentiment towards their campaigns.

6. Lastly, it is important to consider election-specific factors. Each election may have unique circumstances such as political climate, incumbent advantage, key issues, or local dynamics that can significantly influence the outcome. Gathering information on these specific factors and their potential impact on the candidates' chances of winning is important for a comprehensive analysis.

7. By collecting and analyzing this diverse range of data, one can make a more informed comparison of the likelihoods of two candidates winning their elections, even when they are running in different contexts. It is important to note that while data analysis provides valuable insights, election outcomes can still be influenced by unforeseen events, changing circumstances, and individual voter decisions.

Learn more about Demographic information here: brainly.com/question/32038732

#SPJ11

The volume of the object is 285 cubic feet based on the individual volume of cylinder and rectangular prism.

We will calculate the volume of each shape individually followed by their addition.

To calculate the volume of cylinder, we will find radius.

Radius = diameter/2

Radius = 4/2

Radius = 2 ft

Volume of cylinder = πr²h, where r is radius and h is height. Keep the values in formula -

Volume of cylinder = 3 × 2² × 5

Take square and multiply the digits

Volume of cylinder = 60 cubic feet

Volume of rectangular prism = l × w × h, where l is length, w is width and h is height

Volume of rectangular prism = 5 × 5 × 9

Volume = 225 cubic feet

Total volume = 60 + 225

Total volume = 285 cubic feet

Hence, the volume of object is 285 feet.

Learn more about volume -

https://brainly.com/question/1972490

#SPJ1

This option represents a correct sequence of steps in the conventional research model, starting with forming a hypothesis, then designing the research, followed by collecting data, and finally analyzing the data.

The correct sequence of steps in the "conventional" research model is D) Hypothesis formation, research design, data collection, data analysis. The first step is to form a hypothesis or a tentative explanation for the phenomenon being studied. The next step is to design the research study to test the hypothesis. This includes selecting the sample, determining the variables to measure, and deciding on the research methods.

Once the research design is finalized, data collection can begin. This involves gathering data using various techniques such as surveys, interviews, or experiments. Finally, data analysis is performed to examine the data and determine if the results support or refute the hypothesis.
Your answer: D) Hypothesis formation, research design, data collection, data analysis

To know more about Sequence  click here.

brainly.com/question/30262438

#SPJ11

The surface area of the sphere is 1133.54cm² and sinθ  = 5/13, cosθ = 12/13 and tan θ = 5/12 respectively.

The surface area of a sphere is defined as the region covered by its outer surface in three-dimensional space.  A Sphere is a three-dimensional solid having a round shape, just like a circle. The formula of total surface area of a sphere in terms of pi (π) is given by:

S.A = 4πr²

In the given question;

radius = diameter / 2

radius = 19 / 2

radius = 9.5cm

The surface area = 4 * 3.14 * 9.5²

S.A = 1133.54cm²

17.

To find the value of sinθ, cosθ and tanθ, we need to apply trigonometric ratio;

sinθ = opposite / hypothenuse

hypothenuse = ?

Using Pythagorean theorem;

x² = 5² + 12²

x = 13

sinθ = 5/13

cosθ = 12/13

tan θ = 5/12

Learn more on surface area of sphere here;

https://brainly.com/question/12377470

#SPJ1

the probability of experiencing neither side effect is 0.37 or 37%.let's denote the probability of experiencing nausea by P(n) and the probability of experiencing decreased sexual drive by P(d). We know that:

P(n) = 0.23
P(d) = 0.52
P(n ∩ d) = 0.12

We want to find the probability of experiencing neither side effect, which can be denoted by P(~n ∩ ~d), where ~n and ~d represent the complements of nausea and decreased sexual drive, respectively.

We can use the formula for the probability of the union of two events to find P(~n ∪ ~d):

P(~n ∪ ~d) = 1 - P(n ∪ d)

We know that P(n ∪ d) = P(n) + P(d) - P(n ∩ d), so we can substitute the given values to get:

P(n ∪ d) = 0.23 + 0.52 - 0.12 = 0.63

Therefore,

P(~n ∪ ~d) = 1 - 0.63 = 0.37

So the probability of experiencing neither side effect is 0.37 or 37%.

To  learn  more about probability click here:brainly.com/question/32117953

#SPJ11

The probability that the Islanders will win at most two out of six games in a series against the Rangers is approximately 0.107, or 10.7%

We have,

This is a binomial probability problem with n = 6 trials and p = 0.83 probability of success (Islanders winning) in each trial.

We want to find the probability of winning at most 2 games, which means we need to calculate the probability of winning 0, 1, or 2 games and add them up.

Using the binomial probability formula, the probability of winning exactly k games out of n is:

P(k) = (n choose k) x p^k x (1 - p)^{n-k}

where (n choose k) is the binomial coefficient.

Using this formula.

P(0) = (6 choose 0) x 0.83^0 x 0.17^6 = 0.001

P(1) = (6 choose 1) x 0.83^1 x 0.17^5 = 0.015

P(2) = (6 choose 2) x 0.83² x 0.17^4 = 0.091

The probability of winning at most 2 games.

P(0 or 1 or 2)

= P(0) + P(1) + P(2)

= 0.107

Therefore,

The probability that the Islanders will win at most two out of six games in a series against the Rangers is approximately 0.107, or 10.7%

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.

Taking the derivative of the numerator:

d/dθ [1 - sin(θ)] = -cos(θ)

Taking the derivative of the denominator:

d/dθ [1 + cos(6θ)] = -6 sin(6θ)

Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))

When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:

= 0 / (-6)

= 0

Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.

The functions y = 8•2ˣ and y = 8•2ˣ are equivalent using the laws of exponents

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

y=2*+³ and y=8•2*

Express properly

So, we have

y = 2ˣ ⁺ ³ and y=8•2ˣ

When the first function expression is expanded, we have

y = 2ˣ * 2³ and y=8•2ˣ

Evaluate the exponent

y = 2ˣ * 8 and y=8•2ˣ

So, we have

y = 8•2ˣ and y = 8•2ˣ

hence, the functions are equivalent using the laws of exponents

Read mroe about expressions at

https://brainly.com/question/30492964

#SPJ1

Answer: 4.5

Step-by-step explanation: We can find the answer to this using toa (Tanjent). We’d start with tan(75)= 17/x. From here we’d multiply both sides by x to get xtan(75) = 17. Now we’d just have to divide both sides by tan(75) to get 4.5.

The average rate of change in the time it takes sound to travel 1 kilometer is 2.995 seconds.

Given that, the time t(in seconds) it takes for sound to travel 1 kilometer can be modeled by t=1000/(0.6T+331), where T is the air temperature (in degree Celsius)

1) Given that, you hear the thunder 2.9 seconds later.

Here, 2.9=1000/(0.6T+331)

2.9(0.6T+331)=1000

1.74T+959.9=1000

1.74T=1000-959.9

1.74T=40.1

T=40.1/1.74

T=23.045° Celsius

2) Here, T=0° Celsius and T=10° Celsius

2.9=1000/(0.6T+331)

t=1000/(0.6×0+331)

t=1000/331

t=3.02 seconds

Where, T=10

t=1000/(0.6×10+331)

t=1000/337

t=2.97

So, average time = (3.02+2.97)/2

= 2.995 seconds

Therefore, the average rate of change in the time it takes sound to travel 1 kilometer is 2.995 seconds.

Learn more about the temperature here:

https://brainly.com/question/11464844.

#SPJ1

Nina planted 24 pink and purple tulips. If 1/3 of the tulips were pink. Nina planted 8 pink tulips and 16 purple tulips.

Nina planted a total of 24 pink and purple tulips. Given that 1/3 of the tulips were pink, we can use this information to determine the number of pink tulips planted.

To find the number of pink tulips, we need to multiply the total number of tulips by the fraction that represents the proportion of pink tulips. In this case, the fraction that represents the proportion of pink tulips is 1/3, which can also be expressed as 8/24 (since 1/3 is equivalent to 8/24).

To find the number of pink tulips, we can multiply the total number of tulips (24) by the fraction 8/24, which gives us the answer:

Number of pink tulips = 24 x 8/24 = 8

Therefore, Nina planted 8 pink tulips. We can also find the number of purple tulips by subtracting the number of pink tulips from the total number of tulips, which gives us:

Number of purple tulips = 24 - 8 = 16

So, Nina planted 8 pink tulips and 16 purple tulips.

Learn more about planted here

https://brainly.com/question/29786728

#SPJ11

The most commonly shaped base in pin curls is the rectangular base.

This is the main answer to your question. An explanation for this is that the rectangular base is versatile and can be used for creating various sizes of curls. Additionally, it allows for easy control of the curl direction. In conclusion, when creating pin curls, the rectangular base is the most commonly used due to its versatility and ease of use.


The arc base, also known as the half-moon or C-shape base, is the most popular base shape for pin curls because it allows for better distribution of the hair and provides more natural-looking curls. This shape helps prevent splits in the finished hairstyle, ensuring a smoother and more cohesive appearance.

In pin curls, the arc base is the most commonly used base shape due to its ability to create natural-looking curls and prevent splits in the hairstyle.

To know more about rectangular visit:

https://brainly.com/question/21308574

#SPJ11

In a net of a solid, the number of faces meeting at each vertex can be determined by examining the net and counting the number of lines that meet at each vertex. Each line corresponds to an edge of a face, so the number of lines meeting at a vertex is equal to the number of faces meeting at that vertex.

For example, if we consider a cube net, we can see that three faces meet at each vertex. Therefore, a cube has three faces meeting at each vertex.

Similarly, for other solids, we can count the number of faces meeting at each vertex by examining the net. For example, for a regular tetrahedron, four faces meet at each vertex; for a regular octahedron, four faces meet at each vertex; for a regular dodecahedron, three faces meet at each vertex; and for a regular icosahedron, five faces meet at each vertex.

To learn more about vertex : brainly.com/question/13921516

#SPJ11

A number which is subtracted by 3 from it first and the total then divided by 8, which results in 4 is 35

Let's the number we're trying to find be "x".

So, according to the problem, if we subtract 3 from x first, we get,

x - 3

Then, if we divide that total by 8, we get 4:

(x - 3) / 8 = 4

Now, we can solve for x by isolating it on one side of the equation. First, we can multiply both sides of the equation by 8:

x - 3 = 32

x = 35

So, the number is 35

To know more about Equations here

https://brainly.com/question/10413253

#SPJ1

Answer:

A) d=120 x m

Step-by-step explanation:

This equation expresses the linear relationship between the total cost of Jake's guitar lessons (d) and the number of months he takes lessons (m). The constant of proportionality in this equation is 120, which is the monthly cost of the lessons. To find the total cost of the lessons, we simply multiply the monthly cost by the number of months.

The height of the 1-cup measuring cylinder with a radius of 2 inches is approximately 1.1508 inches.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

We know that 1 cup is equal to 14.4375 in^3. So, we can set up an equation:

14.4375 = π(2)^2h

Simplifying, we get:

14.4375 = 4πh

Dividing by 4π, we get:

h = 14.4375 / (4π) ≈ 1.1508 inches

Therefore, the height of the 1-cup measuring cylinder with a radius of 2 inches is approximately 1.1508 inches.

Learn more about cylinder here

https://brainly.com/question/27440983

#SPJ11

The correct answer is option A - True. An array is a data structure in programming that allows you to store a collection of values of the same data type in a single variable.

Each value is assigned an index number, starting from 0, which represents its position in the array.  Arrays are useful in programming because they allow you to store and manipulate multiple values using a single variable. This can help simplify code and make it more efficient.

For example, if you wanted to store the grades of 10 students in a program, you could create an array of 10 elements and assign each grade to a specific index in the array.  In addition to storing data, arrays can also be used to perform calculations and manipulate data.

For example, you could use a loop to iterate through an array and calculate the average of all the values stored in the array. Overall, arrays are a powerful tool in programming that can help you organize and manipulate data.

By thinking of an array as a collection of variables contained within a single variable, you can better understand how arrays work and how to use them effectively in your programs.

To know more about variable click here

brainly.com/question/2466865

#SPJ11

Thus,  the vector perpendicular to [4, -2, -3] can be represented as [2]s + [-2]t.

The statement about the vectors being perpendicular if x + y = 0 is incorrect.

Two vectors are called perpendicular if their dot product is 0, not their sum.

To find a vector perpendicular to [4, -2, -3], you can use the cross product, which is calculated as follows:

Let the perpendicular vector be [a, b, c] = [u]s + [v]t. We need to find the values of a, b, and c such that the dot product of [4, -2, -3] and [a, b, c] is 0:
4a - 2b - 3c = 0

Since you're looking for an answer in the form of [ ]s + [ ]t, we can represent the perpendicular vector as:
[a, b, c] = [u]s + [v]t

An example of a perpendicular vector to [4, -2, -3] is [2, -2, 4]. We can write this as:
[2, -2, 4] = [2]s + [-2]t

This means the vector perpendicular to [4, -2, -3] can be represented as [2]s + [-2]t.

Know more about the dot product

https://brainly.com/question/30404163

#SPJ11

Answer: (50, -40)

Step-by-step explanation:

You can find the slope if you want, but this is pretty simple to find just by noticing that the point C is directly in the middle of A + B.

Please mark brainliest!!

If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

If you invest $3000 in an account that pays simple interest of 4% for 30 years, the amount of money you'll have at the end of 30 years can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
In this case, Principal = $3000, Rate = 4%, and Time = 30 years
Interest = 3000 x 0.04 x 30 = $3600
Therefore, the total amount of money you'll have at the end of 30 years will be the sum of the principal and interest:
Total Amount = Principal + Interest = $3000 + $3600 = $6600
It's important to note that the interest earned in a simple interest account does not compound over time, meaning you earn the same fixed interest rate each year. If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

To know more about simple interest visit :

https://brainly.com/question/20406888

#SPJ11

The coefficient of x² in the expansion of (3x - 1)5  IS: D) -90.

Make use of  the binomial theorem formula to find the coefficient of x².

(a + b)ⁿ = Σ[n choose k] [tex]a^(n-k) * b^k[/tex]

Where:

a represent 3x

b represent -1

n represent  5

k represent 0, 1, 2, 3, 4, 5

n choose k represents  binomial coefficient,

So,

(3x - 1)⁵ = Σ[5 choose k] [tex](3x)^(5-k) * (-1)^k[/tex]

= (3x)⁵ - 5(3x)⁴ + 10(3x)³ - 10(3x)² + 5(3x) - 1

Thus:

-10(3x)².

-10*3²

= -90

Therefore the coefficient of x² is option D.

Learn more about coefficient of x² here:https://brainly.com/question/30243003

#SPJ1

Without knowing the total cost of the wallpaper or the dimensions of the rectangular prism, it is not possible to determine the cost of the wallpaper per square foot.

To calculate the cost per square foot, we would need to know the total cost of the wallpaper and the total area covered by the wallpaper. Since we do not have this information, we cannot determine the cost per square foot.

In summary, the cost of the wallpaper per square foot cannot be determined without knowing the total cost of the wallpaper and the dimensions of the rectangular prism that Lamar built.

To learn more about prism click here, brainly.com/question/12649592

#SPJ11

The probabilities are P(a golf ball then a basketball) is 0.0451, P(a football then a baseball) is 8.33%, P(basketball, then not a football) is 0.0864 and  P(two baseballs) is 0.15.

For the first probability, we want to find the probability of drawing a golf ball first and a basketball second. There are a total of 25 balls in the bag, so the probability of drawing a golf ball first is 3/25. After drawing a golf ball, there are 22 balls left in the bag, including 3 basketballs.

Therefore, the probability of drawing a basketball second is 7/22. Since we want both events to occur, we multiply the probabilities together to get:

P(a golf ball then a basketball) = 3/23 * 7/22 ≈ 0.0451

For the second probability, we want to find the probability of drawing a football first and a baseball second. There are a total of 25 balls in the bag, so the probability of drawing a football first is 5/25.

After drawing a football, there are 24 balls left in the bag, including 10 baseballs. Therefore, the probability of drawing a baseball second is 10/24. Since we want both events to occur, we multiply the probabilities together to get,

P(a football then a baseball) = 5/25 * 10/24

= 1/12

= 0.0833

In percentage it will be 8.33%.

For the third probability, we want to find the probability of drawing a basketball first and then any ball that is not a football. There are a total of 25 balls in the bag, so the probability of drawing a basketball first is 3/25.

After drawing a basketball, there are 24 balls left in the bag, including 5 footballs. Therefore, the probability of not drawing a football second is (24-5)/24 = 19/24. Since we want both events to occur, we multiply the probabilities together to get,

P(basketball, then not a football) = (3/25) * (1 - 5/24)

= 0.0864

For the fourth probability, we want to find the probability of drawing two baseballs. There are 10 baseballs in the bag, so the probability of drawing a baseball first is 10/25. After drawing a baseball, there are 9 baseballs left in the bag out of a total of 24 balls.

Therefore, the probability of drawing another baseball second is 9/24. Since we want both events to occur, we multiply the probabilities together to get:

P(two baseballs) = 10/25 * 9/24

= 3/20

= 0.15

To know more about probability, visit,

https://brainly.com/question/13604758

#SPJ1

In Fechner's Law, as one variable increases arithmetically, the other variable increases geometrically.

In Fechner's Law, as one variable increases arithmetically, the other variable increases: b. geometrically.

Fechner found in his research that different people have different sensitivities to certain stimuli. For example, the ability to see differences in light can affect the quality of a person's vision. It has also been noted that people are sensitive to changes in stimuli due to emotional impact. He used this to create another version of Weber's law, which he called die Maß formel, or "measurement formula." Fechner's law states that the force of thought is proportional to the logarithm of the force.

If the intensity of the stimulus is tripled (eg 3×1), the sensitivity doubles from its original value (eg 1+1).

If the intensity of the stimulus is tripled again (eg 3×3×1), the corresponding sensitivity will be three times its original value (eg 1+1+1).

So, for the stimulus intensity to double, the perceived intensity only increases.

Learn more about Geometrically:

brainly.com/question/31707452

#SPJ11

part (a) is that the speed of the car was 80 mph.

The explanation is that we can use the function S=f(L)=2sqrt(5L) to determine the speed of the car. Plugging in L=320, we get S=2sqrt(5*320)=80 mph.
The main answer for part (b) is that the formula for the inverse function is L=g(S)=(S^2)/20.
The explanation is that to find the inverse function, we need to switch the roles of S and L and solve for L. Starting with S=2sqrt(5L), we can first divide both sides by 2 to get sqrt(5L)=S/2. Then, we square both sides to get 5L=(S^2)/4. Finally, we solve for L to get L=g(S)=(S^2)/20.

The main answer for part (c) is that the skid marks would be 200 feet long.

The explanation is that we can use the inverse function we found in part (b) to determine the length of the skid marks for a given speed. Plugging in S=50, we get L=(50^2)/20=1250/20=62.5 feet. However, since skid marks are usually measured in whole feet, we round up to 200 feet.

To learn more about function visit:

https://brainly.com/question/21145944

#SPJ11