7x^4 -36x^3+61x^2-36x+4
What are the real solutions of the equation

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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For the function F(x)=1/x-2, if x is close to 2 then the value of F(x) may be 10000.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y.

We have to find the value of function when x is close to 2. Let the number which closes to 2 is 2.0001. Put the value of x in the function to find the value of function.

F(x)=1/x-2

=1/2.0001-2

=1/0.0001

=10000

Hence for the function F(x)=1/x-2 the value of function could be 10000 if x is close to 2.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Based on the given information the three correct statements when comparing the experimental and theoretical probabilities for Mary Jane's spinner are option A, C, and D.

Here's a brief breakdown for each statement:
A. The theoretical probability for landing on the star is greater than the experimental probability.

If the spinner is fair, the theoretical probability of landing on each symbol is equal (50% for star and 50% for heart). Since the experimental probability of landing on the star is 6/15, the theoretical probability is greater.

C. As the number of spins increases, the closer the experimental probability will get to the theoretical probability.

According to the Law of Large Numbers, as the number of spins increases, the experimental probability will get closer to the theoretical probability, assuming a fair spinner.

D. The experimental probability for landing on the heart is greater than the theoretical probability.
The experimental probability for landing on the heart is 9/15, which is greater than the theoretical probability of 50%.

Therefore, option A, C, and D are the correct one.

Complete Question

Mary janes spins the spinner 15 times. The arrow lands 6 times on a star and 9 times on the heart. Which THREE statements are correct when comparing the experimental and theoretical probabilities?

A. The theoretical probability for landing on the star is greater than the experimental probability.

B. The experimental probability for landing on the heart is less than the theoretical probability.

C. As the number of spins increases, the closer the experimental probability will get to the theoretical probability.

D. The experimental probability for landing on the heart is greater than the theoretical probability.

E. The experimental probability for landing on the star is greater than the theoretical probability.

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To compare the experimental and theoretical probabilities, we need to know the theoretical probabilities of landing on the star and heart.

If the spinner is fair, then the theoretical probability of landing on the star is 1/3 and the theoretical probability of landing on the heart is 2/3.

Comparing experimental and theoretical probabilities:

The experimental probability of landing on the star is 6/15 = 2/5, while the theoretical probability is 1/3. This means that the experimental probability is higher than the theoretical probability.

The experimental probability of landing on the heart is 9/15 = 3/5, while the theoretical probability is 2/3. This means that the experimental probability is lower than the theoretical probability.

The sum of the experimental probabilities of landing on the star and heart is 2/5 + 3/5 = 1, which is also the sum of the theoretical probabilities. This means that the probabilities add up to 1, as they should.

Therefore, the correct statements are:

The experimental probability of landing on the star is higher than the theoretical probability.

The experimental probability of landing on the heart is lower than the theoretical probability.

The sum of the experimental probabilities add up to 1, as they should.

The equation of line in slope-intercept form is,

Here, m is slope of line and c is y-intercept.

Simplify the equation to obtain the slope-intercept form.

The value of x from the given linear function is -48

Linear equations are equation that has a leading degree of 1. For instance the equation y = mx + b is a linear equation.

Given the equation below

-x/3 + 4 =20

We are to determine the value of x

Subtract 4 from both sides to have;

-x/3 + 4 - 4 = 20 - 4

-x/3 =20 - 4

-x/3 = 16

Multiply both sides by 3 to have

-x = 3(16)

-x = 48

x = -48

Hence the value of x from the given linear function is -48

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To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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Answer: if the boat costs 12,500 and raises by 7 percent a year.

Step-by-step explanation:

7 percent of 12,500 is 875 and if it kept raising for 18 years we would multiply 875 X 18 which equals 15750 and then we would add the original which would give us 28250$

so the answer is 28250$

The ethnicity of respondents in a political poll of randomly selected adults is an example of a categorical variable.

A categorical variable is a type of variable that represents data that can be categorized into distinct groups or categories. In this case, the ethnicity of the individual respondents in the political poll represents different categories such as Asian, African American, Hispanic, Caucasian, etc. Each respondent falls into one of these categories based on their ethnicity.

The variable is categorical because it does not have numerical values that can be quantified or measured. Instead, it represents qualitative data that can be described using labels or categories.

Therefore, the ethnicity of the individual respondents in a political poll of randomly selected adults is an example of a categorical variable.

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Answer:

it would be 324 divided by 18. since 18 to the 2nd power is 324.

Answer:

c=d-ab

Step-by-step explanation:

ab+c=d

move over to the other side

change sides change signs

c=d-ab

Answer:

c=d−ab

Subtract ab from both sides of the equation

Answer:

see explanation

Step-by-step explanation:

Given that y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

(a)

To find k use the condition y = 6, x = 2, then

6 = 2k ( divide both sides by 2 )

k = 3

y = 3x ← equation of proportion

(b)

When x = 7, then

y = 3 × 7 = 21

(c)

When y = 30, then

30 = 3x ( divide both sides by 3 )

x = 10

Answer: (a) k = 3

               (b) y = 21

               (c) x = 10

Step-by-step explanation:

Directly proportional uses the formula: y = kx

(a) Given y = 6 and x = 2, find k.             6 = k(2)

                                                                 3 = k

(b) Given k = 3 and x = 7, find y.             y = kx

                                                                y = 3(7)

                                                                y = 21

(c) Given k = 3 and y = 30, find x.           y = kx

                                                               30 = 3x

                                                                10 = x

This problem involves finding various properties of two random variables, X and Y, and a new random variable Z = X + Y. We are asked to find the mean and variance of X - 3Y, the probability that Y ≥ X, the conditional joint PDF of X and Y given Y ≥ X, the PDF of Z, a sketch of the conditional PDF of Z given Y = 3, E[Z | Y = y] and E[Z | Y], the joint PDF fZ,Y of Z and Y, and the probability of "heads" given that W = 3, where W is a new random variable based on a coin toss and Y.

In this problem, we first find the mean and variance of X - 3Y, using the properties of the uniform and exponential distributions. Next, we find the probability that Y ≥ X, which involves integrating the joint PDF of X and Y over the region where Y ≥ X. This probability is denoted by c and is used in subsequent parts of the problem.

We then find the conditional joint PDF of X and Y given that Y ≥ X, which involves normalizing the joint PDF of X and Y over the region where Y ≥ X. This is denoted by fX,Y | Y≥X (x,y) and can be expressed in terms of the constant c from the previous part. Next, we find the PDF of Z = X + Y, which involves convolving the PDFs of X and Y. We also sketch the conditional PDF of Z given Y = 3, which involves finding the PDF of X + 3 given that Y = 3.

Finally, we find E[Z | Y = y] and E[Z | Y], which involve finding the conditional expectations of Z given Y = y and the marginal expectation of Z with respect to Y. We also find the joint PDF fZ,Y of Z and Y, which involves using the properties of the convolution to find the PDF of Z and then finding the joint PDF of Z and Y. Finally, we find the probability of "heads" given that W = 3, which involves finding the conditional probabilities of the coin toss given Y = 1 and Y = 1/2, and then using Bayes' rule to find the desired probability.

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You can use the fact that only the like terms of the polynomial get added or subtracted by adding or subtracting their coefficients.

The reduced form of the given polynomials' subtraction is given by

Option B: \(11y - 10 + 2y^2\)

Those terms which have same variables raised with same powers.

For example,

\(6x^2\) and \(5x^2\) are like terms since variable is same, and it is raised to same power 2.

For example

\(4x^3\) and \(5x\) are not like terms as the variables are same but powers aren't same.

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in

\(10x^2\)

we have 10 as coefficient of  \(x^2\)

Suppose we have \(5x^2 + 6y\) . Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.

If we have, suppose, \(4x + 5x^2 + 2x\), then we see that 4x and 2x are like terms, their coefficient can be added and thus, the simplified form would be \((4+2)x + 5x^2 = 6x + 5x^2\)

The given polynomials to be subtracted are

\(7y +2y^2 - 7\: \rm by\: 3 - 4y\)

The subtraction will be done as:

\(\begin{aligned}7y + 2y^2 - 7 - (3-4y) &= 7y + 2y^2 - 7 - 3 + 4y \\&= (7+4)y + 2y^2 -7-3 \\&= 11y + 2y^2 - 10\\\end{algned}\)

Thus, the reduced form of the given polynomials' subtraction is given by

Option B: \(11y - 10 + 2y^2\)

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Option d. The approximate probability that a randomly selected student is satisfied with their school's variety of extracurricular activities is 0.658.

To find the probability that a randomly selected student is satisfied with their school's variety of extracurricular activities, we need to determine the number of satisfied students out of the total number of students surveyed.
From the table provided, we can see that 37 students from High School A and 42 students from High School B were satisfied. So, the total number of satisfied students is 37 + 42 = 79. The total number of students surveyed is 120 (60 from each school).
Now, we can calculate the probability by dividing the number of satisfied students by the total number of students surveyed:
Probability = (Number of satisfied students) / (Total number of students surveyed)
Probability = 79 / 120
This results in an approximate probability of 0.658.
Therefore, the approximate probability that a randomly selected student is satisfied with their school's variety of extracurricular activities is 0.658 (option D).

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The standard normal distribution has the largest variance.

The variance of a normal distribution determines the spread or dispersion of the data.

A larger variance indicates a wider spread of values around the mean. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a variance of 1. Since the variance is fixed at 1 for the standard normal distribution, it has the largest variance compared to any other normal density with different variances.

The variance of a normal distribution measures how much the data values deviate from the mean.

It is calculated as the average of the squared differences between each data point and the mean. A higher variance implies a greater dispersion of values, indicating a wider range of possible outcomes.

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Answer:

Step-by-step explanation:

You have shaded 4/7=8/14

6/7=12/14

So you need to shade 12 boxes

Answer:

Negative 1/300

Step-by-step explanation:

I took the qiuz

Answer:

The average cost of a movie ticket in Japan is $17.86 and the average cost of a movie ticket in Switzerland is $13.75

Step-by-step explanation:

The question seems to be incomplete. Here is a similar question and the solution:

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost  ​$81.08 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost  $76.97. How much does an average movie ticket cost in each of these countries?

Step-by-step explanation:

Let the cost of tickets in Japan be $x and the cost of tickets in Switzerland be $y.

From the question,

It would cost  ​$81.08 to buy three tickets in Japan plus two tickets in Switzerland. That is

3x + 2y = 81.08 ...... (1)

Also from the question,

Three tickets in Switzerland plus two tickets in Japan would cost  $76.97. That is

2x + 3y = 76.97 ...... (2)

Multiply equation (1) by 2, so that we get

6x + 4y = 162.16 ...... (3)

and multiply equation (2) by 3, so that we get

6x + 9y = 230.91 ...... (4)

Now, Subtract equation (3) from equation (4), we get

5y = 68.75

y = 68.75/5

y = 13.75

Put the value of y into equation (1) to determine x

3x + 2y = 81.08

3x + 2(13.75) = 81.08

3x + 27.5 = 81.08

3x = 81.08 - 27.5

3x = 53.58

x = 53.58/3

x = 17.86

∴ x = 17.86 and y =13.75

Hence, the average cost of a movie ticket in Japan is $17.86 and the average cost of a movie ticket in Switzerland is $13.75.

Answer:

11cm

Step-by-step explanation:

You have to add them all up

Answer:

1, 3, 5, 9, 15, 27, 45, 135.

Step-by-step explanation:

Answer:

The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135

Answer:

No Solutions

Step-by-step explanation:

The two points are (3,2) and (-2,-2)

Slope is y change over x change.

So... -2-2 over -2-3 equals to -3-(-2) over -2-(-2).

That is -3+2 over -2+2 which is -2 over 0.

You can't divide by zero so the slope is "NoSolutions"

Hope this helps :)

-185/100 = -1.85

a) -1.08 this number id greater than -1.85

b) 190/100 = 1.9 this number is greater than -1.85

c) -35/20 = -1.75 this number is greater than -1.85

All these numbers are greater than -185/100

Answer:

Step-by-step explanation:

5.

volume=l×w×h=8×6×7=336 mi³

6.

diameter=16 yd

radius=16/2=8 yd

\(volume=\frac{4}{3} \pi \times 8^3=\frac{2048}{3} \pi \approx 2144.67 \approx 2144.7 yd^3\)

We have 8 - 0 = 8 other coins which are 3 quarters and 5 nickels.Check:5 * 5 + 3 * 25 = 25 + 75 = 100 cents = $1.00.This is the correct answer.

Let's solve the question step by step. Here's what we know: We have exactly 8 coins. They are worth exactly 63 cents. None of them are 50-cent pieces. Let the number of pennies be x. Let the number of other coins be y. Now we have two equations, according to the information given above: x + y = 8 and x + 5y = 63.We need to solve for x because the question asks for the number of pennies. Substituting x = 8 - y in the second equation:8 - y + 5y = 63Simplifying and solving for y, we get: y = 11Substituting y = 11 in x + y = 8:x + 11 = 8x = -3We can't have a negative number of coins, so our answer is 0 pennies.

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(5(12-2)2+7)/3

(5(10)2+7)/3

(50(2)+7)/3

(100+7)/3

107/3

35.66666...

Answer: $9,779

Step-by-step explanation:

Where:

C is the coupon payment

r is the yield to maturity (expressed as a decimal)

n is the total number of coupon payments

F is the face value or par value of the bond

In this case, the bond has a $10,000 face value, a coupon rate of 7.60% (or 0.076 as a decimal), semiannual coupons, and a yield to maturity of 4.30% (or 0.043 as a decimal). The bond matures in five years, so there will be 10 semiannual coupon payments.

Let's calculate the price: