F(x) = x2 1 What is f(f(x))? x4 2x2 1 x4 2x2 2 x4 2 x4 1.

The described sampling method is an example of random sampling.

The sampling method described in the question is known as simple random sampling, which is a common method of selecting a representative sample from a population.

In this method, each member of the population is assigned a unique number, and a certain number of individuals are selected randomly from the population.

Simple random sampling is a type of probability sampling, which means that each member of the population has an equal chance of being selected for the sample.

This is important because it ensures that the sample is representative of the population as a whole, and reduces the risk of sampling bias.

The process of simple random sampling is straightforward and easy to implement, making it a popular choice for researchers. However, it can be time-consuming and may not be practical for very large populations. In such cases, other sampling methods such as stratified sampling or cluster sampling may be more appropriate.

Overall, simple random sampling is a reliable and effective method of selecting a representative sample from a population, and is widely used in research studies and surveys.

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1. x = π/6 + 2πn/3, for any integer n

2. Is not possible to solve (I think)

3. x = π/4 + πn, for any integer n

Answer:

20% more of cost price, or 30% more of initial selling price

Step-by-step explanation:

Given:

Total money to be obtained:

Money already got:

Money left to obtain:

Product left to sell, worth of:

The difference:

Required selling price increase:

Or compared to initial price, new SP to be increased by 30%

If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.

The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)

The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)

The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)

The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)

Therefore on application of these rules

For Case A

The point will be (-y , x)

For Case B

The point will be (x,y)

Therefore Option B is the answer.

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Answer:

Well, this is not an answer but, i would like do know your grade. ( & WHO'S idea was it to add LETTERS to MATH!?)

Answer:

Step-by-step explanation:

There are no errors.

The conclusion statement is incorrect.

The graph of the solution set is incorrect.

The substitution of x and y values is incorrect.

Answer:

Its C

Step-by-step explanation:

For most Welsh Corgis: 25 ≤ shoulder height (cm) ≤ 30, while the internal skull dimension (d) is unrelated.

The compound inequality relating the estimated shoulder height of a dog to the internal dimension of the skull can be expressed as:

25 ≤ d ≤ 30

In this context, most Welsh Corgis have shoulder heights falling within the range of 25 to 30 centimeters. The internal dimension of the skull, represented by "d" in cubic centimeters, is not directly related to the shoulder height but is likely included in the discussion for reference or comparison purposes. The compound inequality signifies that the internal dimension of the skull should fall within the range of 25 to 30 cubic centimeters.

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Answer:

-3,-2,4,6,13

Step-by-step explanation:

put them in order of increment

Answer:

21 years

Step-by-step explanation:

Lawrence did research on many different swimmers. He graphed each swimmer with a tick on the graph. The more ticks, the higher amount of people. Because most of the ticks are on 21, If I did this right, It should be 21.

Arrange the data in ascending order,

The mean is ,

The mean is 98.6.

The median is,

The median is 96.5.u

The mode is the value that appears most often in a set of data values.

The range is determined as the difference between the maximum and minimum value.

The total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

This question uses the combination and permutation theory. Combinations are used to calculate the total number of ways to assign the three tasks to the 8 people, and permutations are used to multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks.

given below :

1. Calculate the total number of ways to assign the three tasks to the 8 people: 8 x 7 x 6 = 336

2. Multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

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The equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6). Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

The equation given is 3x₁ + 5x₂ = 30. To find the axis intercept, we need to determine the points at which the line intersects the x₁ and x₂ axes. To find the x₁-axis intercept, we set x₂ = 0 and solve for x₁ 3x₁ + 5(0) = 30 3x₁ = 30
x₁ = 10

So, the x₁-axis intercept is (10, 0) which corresponds to point D in the given options. To find the x₂-axis intercept, we set x₁ = 0 and solve for x₂: 3(0) + 5x₂ = 30 5x₂ = 30 x₂ = 6 Therefore, the x₂-axis intercept is (0, 6) which corresponds to point C in the given options. To summarize, the equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6).

In the given options, option A (10, 6) is not an intercept on either axis. Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

Remember, the x₁-axis intercept is found by setting x₂ = 0, and the x₂-axis intercept is found by setting x₁ = 0 in the equation.The correct answer is option D

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The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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The expected number of matchings goes to infinity as N › [infinity].

Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].

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The matrix representation of the operator A is given by:

A = A₀[ 0  -1

      1   0 ]

To find the normalized eigenvectors for this operator, we need to find the eigenvectors and then normalize them.

Let's find the eigenvectors first. We start by finding the eigenvalues λ by solving the characteristic equation:

det(A - λI) = 0

where I is the identity matrix. Substituting the values of A into the equation, we have:

det(A₀[ 0 -1

          1  0 ] - λ[ 1  0

                             0  1 ]) = 0

Expanding this determinant equation, we get:

A₀² - λ² - A₀ = 0

Solving this quadratic equation, we find two eigenvalues:

λ₁ = √(1 + A₀²) and λ₂ = -√(1 + A₀²)

Next, we substitute each eigenvalue back into (A - λI)x = 0 to find the corresponding eigenvectors x.

For λ₁ = √(1 + A₀²), we have:

(A - √(1 + A₀²)I)x₁ = 0

Substituting the values of A and λ, we get:

A₀[ 0 -1

        1  0 ]x₁ - √(1 + A₀²)[ 1  0

                                                  0  1 ]x₁ = 0

Simplifying this equation, we have:

[ -√(1 + A₀²)  -A₀

          A₀    -√(1 + A₀²) ]x₁ = 0

By solving this system of equations, we can find the eigenvector x₁. Similarly, for λ₂ = -√(1 + A₀²), we solve:

[ √(1 + A₀²)  -A₀

         A₀    √(1 + A₀²) ]x₂ = 0

Once we have the eigenvectors, we can normalize them by dividing each vector by its magnitude to obtain the normalized eigenvectors.

Now, let's compute the matrix W, given by Wᵢⱼ = <e^A|eⱼ>:

W = [ <e^A|e₁>  <e^A|e₂> ]

where |eⱼ> represents the eigenvector eⱼ.

To compute the matrix elements, we need to evaluate the inner product <e^A|eⱼ>. We know that e^A can be expressed as a power series:

e^A = I + A + (A²/2!) + (A³/3!) + ...

By substituting the matrix representation of A, we can calculate e^A. Then, we evaluate the inner product between e^A and each eigenvector eⱼ to obtain the elements of the matrix W.

Finally, we have the matrix W, with Wᵢⱼ = <e^A|eⱼ>, computed using the normalized eigenvectors and the exponential of A.

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Answer:

Circumference of semi circle = 116 cm

Step-by-step explanation:

Given:

Diameter of a circle = 28 cm

Find:

Circumference of semi circle

Computation:

Circumference of semi circle = πr + Diameter

Circumference of semi circle = (22/7)(28) + 28

Circumference of semi circle = 88 + 28

Circumference of semi circle = 116 cm

Answer:

When the determinant of a matrix is almost 0, it means that the matrix is close to being singular, which means that its inverse does not exist or is very close to not existing. This has important implications for the solution of systems of linear equations represented by the matrix.

Specifically, if the determinant of a matrix is almost 0, then the matrix is almost singular, which means that its columns are almost linearly dependent. This, in turn, means that the system of equations represented by the matrix has almost linearly dependent equations, which can lead to multiple solutions or no solutions at all.

In terms of the sensitivity of the solution to changes in the constants of the system, a small change in the constants can lead to a large change in the solution when the determinant of the matrix is almost 0. This is because the inverse of the matrix is very sensitive to changes in its entries when the determinant is almost 0.

For example, consider a system of linear equations represented by a matrix A with determinant very close to 0, and let b be the vector of constants on the right-hand side of the equations. Then, the solution to the system can be approximated by the product of the inverse of A (if it exists) and b, that is:

x = A^(-1) b

However, if A is almost singular, then its inverse is very sensitive to changes in its entries, and a small change in b can lead to a large change in x. This can make the solution to the system unreliable and unstable, and can be a source of numerical errors in computations.

Step-by-step explanation:

When calculating a 99% confidence interval with the same sample size (n) compared to a 95% confidence interval, the margin of error will be larger.

Confidence intervals are used to estimate the true population parameter based on a sample. The confidence level represents the probability that the true population parameter falls within the calculated interval. A 95% confidence interval means that there is a 95% probability that the true parameter lies within the interval, leaving a 5% chance of error. Similarly, a 99% confidence interval means that there is a 99% probability that the true parameter falls within the interval, leaving only a 1% chance of error.

To calculate a confidence interval, the margin of error is added and subtracted from the sample statistic (e.g., mean or proportion). The margin of error is influenced by the confidence level and the sample size. A higher confidence level requires a larger margin of error to account for the increased level of certainty.

As the confidence level increases from 95% to 99%, the margin of error also increases. This is because a higher confidence level requires a larger interval to be confident that the true parameter falls within it. Therefore, when calculating a 99% confidence interval with the same sample size (n) compared to a 95% confidence interval, the margin of error will be larger to accommodate the increased level of confidence.

Therefore, the margin of error will be larger when calculating a 99% confidence interval instead of a 95% confidence interval with the same sample size (n).

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A graphical device used for enumerating sample points in a multiple-step experiment is a tree diagram.

A tree diagram is a way of determining probabilities of different outcomes based on numerous different events.

It helps in identifying all the probable outcomes of an experiment and helps in understanding the likelihood of each of these events.

A tree diagram starts with a single root node that is then divided into different branches based on the potential outcomes of an experiment that are mutually exclusive.

These branches then split again into sub-branches until the final potential outcomes of an experiment are reached.

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Answer:

Step-by-step explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle

Applying the definition of the angle formed by perpendicular lines, the measures are:

a = 5

m<ADB = 25°

m<BDC = 65°

When two lines intersect perpendicularly at a point, they form a right angle, which is equal to 90 degrees.

Thus, angle ADC is a right angle. Therefore, angles ADB and BDC are complementary angles. This means that:

m<ADB + m<BDC = 90°

Substitute

3a + 10 + 13a = 90

16a + 10 = 90

16a = 90 - 10

16a = 80

16a/16 = 80/16

a = 5

m<ADB = (3a + 10) = 3(5) + 10 = 25°

m<BDC = 13a = 13(5) = 65°

Thus, applying the definition of the angle formed by perpendicular lines, the measures are:

a = 5

m<ADB = 25°

m<BDC = 65°

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The point where f(x) = k(x) is (7, 10). The correct answer is A) (7, 10).

To find the point where f(x) = k(x), we need to set the two functions equal to each other and solve for x.

f(x) = k(x)

2x - 4 = x + 3

Simplifying the equation:

2x - x = 3 + 4

x = 7

Now that we have found the value of x, we can substitute it back into either f(x) or k(x) to find the corresponding y-coordinate.

Using f(x):

f(7) = 2(7) - 4

f(7) = 14 - 4

f(7) = 10

Therefore, the point where f(x) = k(x) is (7, 10).

The correct answer is A) (7, 10).

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Answer:9 kilometers away from eachother

Step-by-step explanation: they are 9 kilometers away from eachother cuz if you add 4+5 it equals to 9 so they are 9 kilometers away from eachother

This problem presents a situation where Sara's weekly pay check is equal to $125.52, and we need to calculate how much it'd be if another person got paid 3.2 more.

In order to solve this problem, we need to multiply the value for Sara by 3.2. We have:

Kim's weekly pay check would be equal to $400.8

The length of the wire of the same material whose resistance and diameter are 30 ohms and 1.25 mm, respectively is 100 meters.

We are given that the electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. So, we can write this relationship as:

\($$R \propto \frac{L}{d^2}$$\)

where R is the electrical resistance, L is the length of the wire and d is the diameter of the wire. We can replace the proportionality sign with an equal sign and add a constant of proportionality k to obtain the following equation:

\(R = k\frac{L}{d^2}\)

Now we can find the value of k by substituting the given values of R, L, and d in the above equation. So, we have:

\(25 = k\frac{30}{(0.75)^2}\)

\($$k = 25 \times \frac{(0.75)^2}{30}$$\)

k = 0.46875

Now we can use this value of k to find the length of the wire whose resistance and diameter are given as 30 ohms and 1.25 mm, respectively. So, we have:

\(30 = 0.46875\frac{L}{(1.25)^2}\)

\(L = 30 \times (1.25)^2 \times \frac{1}{0.46875}\)

\($$L = 100 \ \text{meters}$$\)

Therefore, the length of the wire of the same material whose resistance and diameter are 30 ohms and 1.25 mm, respectively is 100 meters.

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*see attachment for the scale drawing

Answer:

5⅝ in × 9 in

Step-by-step explanation:

Dimensions of the actual length = 15 ft by (9 + 6 + 9) ft

Dimensions of the actual length = 15 by 24 ft = 15 ft × 24 ft

Using the scale given as ⅜ in = 1 ft, let's find the dimensions of Leah's scale drawing of the outer rectangle.

Multiply each dimension in ft by ⅜ to get the dimension of the outer rectangle's scale drawing:

\( 15 * \frac{3}{8} = \frac{15*3}{8} = \frac{45}{8} = 5\frac{5}{8} \)

\( 24 * \frac{3}{8} = 3 * 3 = 9 in \)

Therefore, the dimensions of the scale drawing of the outer rectangle = 5⅝ in × 9 in

a. The standard error of the mean can be determined using the formula:

Standard error of the mean = population standard deviation / square root of sample size

Plugging in the given values, we get:

Standard error of the mean = 25 / square root of 250
Standard error of the mean = 25 / 15.8114
Standard error of the mean = 1.579 (rounded to 3 decimal places)


The standard error of the mean measures the amount of variability or error that is expected in the sample mean when compared to the true population mean. It is calculated by dividing the population

by the square root of the sample size. In this case, the standard error of the mean is 1.579, indicating that the sample mean of 20 is expected to be off by around 1.579 units from the true population mean.

c. To determine the 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean +/- (critical value) x (standard error of the mean)

The critical value can be obtained from a t-distribution table with n-1 degrees of freedom, where n is the sample size. For a 95% confidence interval and 249 degrees of freedom, the critical value is 1.96.

Plugging in the given values, we get:

Confidence interval = 20 +/- (1.96) x (1.579)
Confidence interval = 20 +/- 3.095
Confidence interval = (16.905, 23.095) (rounded to 3 decimal places)


The confidence interval is a range of values that is expected to contain the true population mean with a certain degree of confidence. In this case, we are 95% confident that the true population mean falls within the range of 16.905 to 23.095. This means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true population mean.

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Answer:

870.48

Step-by-step explanation:

Answer:

870.92

Step-by-step explanation:

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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