I don’t know wich boxes to choose

We're trying to find the total number of faces F = S + H + D. To do this, we can substitute the expressions for V and E into Euler's formula: (S + H + D) - (4S + 6H + 10D)/2 = 2. Multiplying both sides by 6 to eliminate the fractions: 6(S + H + D) - 3(4S + 6H + 10D) = 12. Simplifying the equation: 6S + 6H + 6D - 12S - 18H - 30D = 12. Combining like terms: -6S - 12H - 24D = 12. Divide both sides by -6: S + 2H + 4D = -2

Let's first consider the number of edges that each face of p has. Since p is convex, each face must be a convex polygon. We know that each vertex is contained in exactly one face of each type, which means that each vertex must be the meeting point of at least three faces. Therefore, each face must have at least three edges.
Since each face is either a square, hexagon, or decagon, we know that the sum of the angles of each face is:
- For a square: 360 degrees
- For a hexagon: 720 degrees
- For a decagon: 1440 degrees
Using the formula for the sum of angles in a convex polygon (180(n-2)), we can find the number of sides for each face:
- For a square: 4 sides
- For a hexagon: 6 sides
- For a decagon: 10 sides
Let's assume that p has f faces. Then, the total number of edges in p is:
E = (4 * number of squares) + (6 * number of hexagons) + (10 * number of decagons)
E = 4s + 6h + 10d
On the other hand, we know that the sum of the degrees around each vertex in p is 360 degrees. Each vertex is contained in exactly one face of each type, so the number of vertices in p is equal to the sum of the number of faces of each type. Therefore:
V = s + h + d
Using Euler's formula for polyhedra (V - E + F = 2), we can solve for the number of faces:
F = 2 - V + E/2
F = 2 - (s + h + d) + (2s + 3h + 5d)/2
F = (3s + 5h + 9d - 4)/2
We know that f must be an integer, so 3s + 5h + 9d must be even. This means that either all of s, h, and d are even, or exactly one of them is odd and the other two are even.
Since p is a convex polyhedron, it must satisfy the condition that the sum of the angles around each vertex is less than 360 degrees (otherwise it would be non-convex). We can check that the only possible combination of numbers of squares, hexagons, and decagons that satisfies this condition and the evenness condition is:
- 12 squares, 20 hexagons, and 30 decagons
Therefore, p has a total of:
f = 12 + 20 + 30
f = 62 faces.

learn more about Euler's formula here: brainly.com/question/24300924

#SPJ11

angle CED = 45°

angle EDC = x

angle DCE = 2x

The value of x.

The sum of all the Interior Angles of a triangle is 180°.

x + 2x + 45° = 180°

or, 3x = 180° - 45°

or, 3x = 135°

or, x = 135/3 = 45°

The value of x is 45°.

Answer:

x = 45

Step-by-step explanation:

CDE + CDE + CED =180°

x + 2x + 45 = 180

3x = 135

x = 45

Answer:

Step-by-step explanation:

See image

(6.1) No equilibrium points exist. (6.2) Equilibrium points: \(P_n = 7\) and \(P_n = -4\). (6.3) Equilibrium points cannot be determined. (5.4) Equilibrium points: P(n) = (3 + √5)/2 and P(n) = (3 - √5)/2.

Let's analyze each system individually to determine if equilibrium points exist and find them if they do.

(6.1) \(a_n+1 = 1 + 1/(1 + 1/a_n), where \ a_n > 0:\)

To find equilibrium points, we need to solve for an+1 = an. Let's set up the equation:

\(a_{n+1} = 1 + 1/(1 + 1/a_n)\)

\(a_n = 1 + 1/(1 + 1/a_n)\)

To simplify this equation, we can substitute an with x:

x = 1 + 1/(1 + 1/x)

Multiplying through by (1 + 1/x), we get:

x(1 + 1/x) = 1 + 1/x + 1

Simplifying further:

1 + 1 = 1 + x + 1/x

Combining like terms, we have:

2 = x + 1/x

Now, let's solve for x:

\(2x = x^2 + 1\)

Rearranging the equation:

\(x^2 - 2x + 1 = 0\)

This is a quadratic equation, but it has no real solutions. Therefore, there are no equilibrium points for this system.

(6.2) \(P{n+1} = √(28 + 3P_n):\)

To find equilibrium points, we need to solve for Pn+1 = Pn. Let's set up the equation:

\(P_{n+1 }= √(28 + 3P_n)\)

Pn = √\((28 + 3P_n)\)

To simplify this equation, we can square both sides:

\(Pn^2\) = 28 + \(3P_n\)

Rearranging the equation:

\(P_n^2 - 3P_n - 28 = 0\)

This is a quadratic equation, and we can solve it by factoring:

\((P_n - 7)(P_n + 4) = 0\)

Setting each factor equal to zero, we find:

\(P_n - 7 = 0\\P_n = 7\\P_n + 4 = 0\\P_n = -4\\\)

\((6.3) (an+1)^2 - ln(e^{-an}) + ln(e^{-2/9}):\)

However, this equation does not simplify further or lead to any specific values for an. Therefore, it is not possible to determine the equilibrium points for this system.

\((5.4) P(n+1) = [P(n) - 1]^2:\)

To find equilibrium points, we need to solve for P(n+1) = P(n). Let's set up the equation:

\(P(n+1) = [P(n) - 1]^2\\P(n) = [P(n) - 1]^2\)

To simplify this equation, we can substitute P(n) with x:

\(x = (x - 1)^2\)

Expanding the equation:

\(x = x^2 - 2x + 1\)

Rearranging the equation:

x^2 - 3x + 1 = 0

This is a quadratic equation, but it does not factor nicely. However, we can solve it using the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(1)(1)))/(2(1))

x = (3 ± √(5))/2

So, the equilibrium points for this system are (3 + √5)/2 and (3 - √5)/2.

To know more about equilibrium,

https://brainly.com/question/14794036

#SPJ11

The formula for the Volume(V) of the cylinder is given as,

Given:

Therefore,

Hence, the volume of the cylinder is

Therefore, The null hypothesis is that the proportion of customers who try out the samples being offered is 0.15 or less, while the alternative hypothesis is that the proportion is more than 0.15.

The null hypothesis (H0) for this test is that the proportion of customers who try out the samples being offered is 0.15 or less. The alternative hypothesis (Ha) is that the proportion of customers who try out the samples being offered is more than 0.15.
The researcher wants to test whether the proportion of customers who try out the samples being offered is higher than 0.15, which means the null hypothesis states that the proportion is 0.15 or lower. The alternative hypothesis, on the other hand, suggests that the proportion is greater than 0.15. The researcher will conduct a hypothesis test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
Therefore, The null hypothesis is that the proportion of customers who try out the samples being offered is 0.15 or less, while the alternative hypothesis is that the proportion is more than 0.15.

To know more about probability visit :

https://brainly.com/question/13604758

#SPJ11

Answer:

The answer is that z = 3

Step-by-step explanation:

Once you solve you get z = 3

-8z + 12 = -12         you subtract -12 from both sides to get rid of the positive 12

     -12 = -12

__________

-8z = -24

__     __              divide -8 both sides

-8      -8             two negatives equal a positive

z = 3                  

Step-by-step explanation:

may be

Last one is correct

Answer:

coupons, rebate, and sales

Step-by-step explanation:

Answer:

i^3=i×i×i

Step-by-step explanation:

i^3(means i is multiplying(×) it self 3 times

The measure of line segment BD in the right triangle is 12.

From the image, right triangle ABC and ADE are similar triangle.

Hence, their corresponding side lengths are proportional.

In triangle ABC

Segment AB = ?

Segment BC = 21

Segment AC = 20 + 15 = 35

In triangle ADE

Segment AD = 16

Segment DE = 12

Segment AE = 20

Since, the two right angles are simimilar, we take the ratio of ratio of the correspoinding sides:

AB/BC = AD/DE

Plug in the values

AB/21 = 16/12

Simplify and solve for AB

AB/21 = 4/3

AB × 3 = 21 × 4

AB × 3 = 84

AB = 84/3

AB = 28

Now, to determine line segment BD, subtract length of AD from AB:

BD = AB - AD

BD = 28 - 16

BD = 12

Therefore, segment BD has a length of 12 units.

Learn more about ratios and proportions at :https://brainly.com/question/29774220

#SPJ1

Answer:

D

Step-by-step explanation:

7^-2 = 1/7^2

The negative means you flip it

1/7^2 times 7^6 is 7^6/7^2 (just multiply).

using rules of exponents, 7^6/7^2 is 7^4 (just subtract 2 from 6)

D is the only one that equals 7^4, as 2 times 2 is 4.

Given that Tara and Pablo leave the park at the same time, but in opposite directions. If Pablo travels 9 mph faster than Tara and after 5 hours they are 105 miles apart, we have to find how fast each is traveling.

Let Tara's speed be x mph, and then Pablo's speed is (x + 9) mph. The distance between the two speeds after 5 hours is equal to 105 miles, and we are to find how fast each is traveling. Using the distance formula:
distance = rate × time
Distance traveled by Tara + Distance traveled by Pablo = Total distance
They are travelling in opposite directions so we need to add the speed of Tara and Pablo, which is (x + x + 9) mph, to get the total distance travelled. The distance traveled by Tara = rate × time = x × 5 = 5x miles.
The distance traveled by Pablo = (x + 9) × 5 = 5x + 45 miles
Total distance traveled = Distance traveled by Tara + Distance traveled by Pablo105 = 5x + 5x + 45
Combine like terms10x = 60Divide both sides by 1010x/10 = 60/10Simplifyx = 6Tara's speed is 6 mph, and then Pablo's speed is (6 + 9) mph, which is 15 mph. Tara's speed is 6 mph, and Pablo's speed is 15 mph.

To know more about speed  refer here:

https://brainly.com/question/28224010

#SPJ11

If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

Find out more information about statistical significance here:

https://brainly.com/question/14100967

#SPJ4

Answer:

Step-by-step explanation:

8

The average rate of change of the function on [0,4] is 8.

The type of model that best fits the given situation is; A linear equation  Model

Right inside the local reservoir we will have an initial amount of water A.

Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.

Thus, after t hours, the amount of water in the reservoir is expressed as:

W = A - 500gal * t

This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.

The domain of this model is restricted because we can't have a negative amount of water in the reservoir,  and as such the maximum value of t accepted is: W = 0 = A - 500gal*t

t = A/500 hours

Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }

Read more about Equation model at; https://brainly.com/question/25896797

#SPJ1

a)

b) The slope-intercept definition of the linear function is given as follows:

y = 3x + 3.50.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points on the linear function in this problem are given as follows:

(2, 9.50) and (5, 18.50).

The slope is given by the division of the change in y by the change in x, hence:

m = (18.50 - 9.5)/(5 - 2)

m = 9/3

m = 3.

Representing the hourly charge.

Hence:

y = 3x + b.

When x = 2, y = 9.50, hence the intercept b, representing the rental fee, is given as follows:

9.5 = 3(2) + b

b = 3.50.

Meaning that the function is defined as follows:

y = 3x + 3.5.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

Answer:

The expected value is -$126- you should not buy the warranty.

Step-by-step explanation:

You will pay $350 for a warranty that pays $2800, therefore the net value is $2800 - $350.

E(x)= (2800-350)(.8)+(-350)(.92)= -126

Answer:

add 5 to both sides

Step-by-step explanation:

thats it the reason why

Answer:

1st option will be the answer.

Answer: 50 miles per hour (mph)

Step-by-step explanation:

150 divided by 3 is 50

150 represents miles ran

3 hours represents time it took to run

Answer:

1.2m

Step-by-step explanation:

60mins is an hour

60 x 3

180

180/150

1.2

Logistic Regression is preferred over Linear Regression for classification problems for several reasons.

Firstly, the predicted values in Logistic Regression are much more interpretable as they lie in the range of 0 to 1, which represents the probability of a certain outcome occurring. In contrast, Linear Regression predicts continuous values which are difficult to interpret as probabilities.
Secondly, the sigmoid curve used in Logistic Regression fits the data better than a straight line used in Linear Regression. This is because the sigmoid curve captures the non-linear relationships between the input variables and the output variable, which is often the case in classification problems.
Lastly, Logistic Regression uses maximum likelihood estimation to estimate parameters, whereas Linear Regression minimizes the mean squared error. Maximum likelihood estimation is a more appropriate method for estimating parameters in classification problems as it takes into account the binary nature of the output variable. Linear Regression, on the other hand, does not consider this binary nature and may not produce accurate results in classification problems.

In summary, Logistic Regression is preferred over Linear Regression for classification problems because of its interpretable predicted values, better fit to non-linear relationships, and appropriate method of estimating parameters using maximum likelihood estimation.

We prefer Logistic Regression over Linear Regression for classification problems for the following reasons:

1) Predicted values in Logistic Regression are more interpretable as they lie in the range of 0 to 1, representing probabilities of class membership, while Linear Regression predicts continuous values which may not directly indicate class membership.

2) The sigmoid curve in Logistic Regression fits the data better for classification problems, as it represents a natural threshold between classes, while a straight line from Linear Regression may not provide clear separation between classes.

3) Logistic Regression uses maximum likelihood estimation to estimate parameters, which makes it more suitable for classification problems as it finds the best fit for the probability of class membership. Linear Regression minimizes the mean squared error, which focuses on minimizing the distance between predicted and actual values, but does not directly optimize for class membership probabilities.

Learn more about Linear Regression:

brainly.com/question/29665935

#SPJ11

Answer:

5). 4×4×3

6). 5×2×2

7). 11×3×2

8). 17×2

Step-by-step explanation:

These are the prime factorizations.

Answer:

162

Step-by-step explanation:

The number of gold coins you have is 162

Let

the number of treasure chest = x

He tried to put 18 gold coins in each treasure chest, but that left 4 treasure chests empty.  Therefore,

So he puts 12 gold coins in each treasure chest but then had 6 coins extra. Therefore,

18x - 72 = 12x + 6

18x - 12x = 6 + 72

6x = 78

divide both sides by 6

x = 78 / 6

x = 13

Therefore, the number of gold coins can be computed as follows:

learn more on algebra here: https://brainly.com/question/14405703

Step-by-step:

\(3\frac{1}{2}+2\frac{3}{5} = \frac{7}{2} + \frac{13}{5} = \frac{35}{10}+\frac{26}{10} = \frac{61}{10}.\)

Explaination:

Use  \(a\frac{x}{y} = \frac{a.y+x}{y}\) to convert a mixed number to a fraction.

Use \(\frac{a}{b} +\frac{x}{y} = \frac{a.y}{b.y}+\frac{b.x}{b.y} = \frac{a.y+b.x}{b.y}\) to calculate the sum of two fractions with different denominators.

Hope this help!

Answer:

y = -3/2 x + 3

-3/2

2/3

y - 1 = (2/3)x

Step-by-step explanation:

Answer:

1.x,y is the answer to first question

2.y=2x+5

The eigenvalues of the matrix A are λ1 = 5 + 4i and λ2 = 5 - 4i, and the corresponding eigenvectors are v1 = [1, 3 + 4i] and v2 = [1, -3 + 4i].

To find the eigenvalues and eigenvectors of the matrix

A = [[2, 1], [-25, 8]]

we need to solve the characteristic equation, which is given by

det(A - λI) = 0

where λ is the eigenvalue and I is the identity matrix.

Let's proceed with the calculations:

A - λI = [[2 - λ, 1], [-25, 8 - λ]]

Now we calculate the determinant of A - λI:

det(A - λI) = (2 - λ)(8 - λ) - (-25)(1)

          = (2 - λ)(8 - λ) + 25

          = λ^2 - 10λ + 16 + 25

          = λ^2 - 10λ + 41

Setting the determinant equal to zero, we have:

λ^2 - 10λ + 41 = 0

To solve this quadratic equation, we can use the quadratic formula:

λ = (-(-10) ± √((-10)^2 - 4(1)(41))) / (2(1))

  = (10 ± √(100 - 164)) / 2

  = (10 ± √(-64)) / 2

  = (10 ± 8i) / 2

  = 5 ± 4i

So the eigenvalues of the matrix A are λ1 = 5 + 4i and λ2 = 5 - 4i.

To find the eigenvectors corresponding to each eigenvalue, we substitute them back into the equation (A - λI)v = 0 and solve for v.

For λ1 = 5 + 4i:

(A - λ1I)v = [[2 - (5 + 4i), 1], [-25, 8 - (5 + 4i)]][[v1], [v2]] = [[-3 - 4i, 1], [-25, 3 - 4i]][[v1], [v2]] = [[0], [0]]

From the first row, we have:

(-3 - 4i)v1 + v2 = 0

v2 = (3 + 4i)v1

We can choose v1 = 1 as a free variable and set v2 = (3 + 4i)v1:

v = [[v1], [(3 + 4i)v1]] = [[1], [3 + 4i]]

Therefore, the eigenvector corresponding to the eigenvalue λ1 = 5 + 4i is v1 = [1, 3 + 4i].

For λ2 = 5 - 4i:

(A - λ2I)v = [[2 - (5 - 4i), 1], [-25, 8 - (5 - 4i)]][[v1], [v2]] = [[-3 + 4i, 1], [-25, 3 + 4i]][[v1], [v2]] = [[0], [0]]

From the first row, we have:

(-3 + 4i)v1 + v2 = 0

v2 = (-3 + 4i)v1

We can choose v1 = 1 as a free variable and set v2 = (-3 + 4i)v1:

v = [[v1], [(-3 + 4i)v1]] = [[1], [-3 + 4i]]

Therefore, the eigenvector corresponding to the eigenvalue λ2 = 5 - 4i is v2 = [1, -3 + 4i].

In summary, the eigenvalues of the matrix A are λ1 = 5 + 4i and λ2 = 5 - 4i, and the corresponding eigenvectors are v1 = [1, 3 + 4i] and v2 = [1, -3 + 4i].

To learn more about eigenvalues click here:

/brainly.com/question/28382500

#SPJ11

Answer:

x          |          y

− 2                − 6

− 1                − 3

0                    0

1                     3

2                    6

hope this helps!

The table of values for the equation y = 3x - 1, is attached.

x y

-2 -7

-1 -4

0 -1

1 2

2 5

3 8

Equations are relations between two or more variables, used to find the value of an unknown variable from the known value of other variables.

We are given the equation y = 3x - 1. We are asked to complete the table, for the given values of x: -2, -1, 0, 1, 2, 3.

To find the y variable, for the given x's, we substitute each value of x, one at a time in the equation.

We put all these values of y, for the corresponding value of x in the table. The completed table is attached.

Learn more about equations at

https://brainly.com/question/4344214

#SPJ2

The times colin and dan take as a ratio is 1 : 3

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

Dan = 1 hour

Collin = 20 minutes

Convert hour to minutes

So, we have

Dan = 60 minutes

Collin = 20 minutes

When expressed as ratio, we have

Collin : Dan = 20 minutes : 60 minutes

Simplify

Collin : Dan = 1 : 3

Hence, teh ratio is 1 : 3

Read more about ratio at

https://brainly.com/question/12024093

#SPJ1