For the given figure, can you conclude mlln? Explain.​

By using the definition of inverse functions we can see that:

a) g(7) = -10

b)(-10,7) is a point on h(x).

c)(7, -10) is a point on j(x)

Remember that if two functions f(x) and g(x) are inverses, then:

f(y) = x

g(x) = y

And also g(f(x)) = x = g(f(x)).

Here we know that functions h(x) and j(x) are inverses, and we also know that:

h(-10) = 7

So for the input -10, we have the output 7.

Then, by using the relation written above, we know that for the inverse function we must have:

j(7) = -10

That is the answer for a.

And for b and c the notation is (input, output), then:

These are the answers of points B and C of the question.

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The mean retirement age in the census report is 68.3 years.

The given information states that the population mean retirement age is 68.3 years, and a random sample of retirement age has a sample mean of 65.8 years. We can use this information to estimate the population mean with a certain level of confidence.

However, the question asks us to find the mean of 68.3 years, which is simply the given population mean. Therefore, we can state that the mean of 68.3 years remains the same, as it is not affected by the sample mean or any other sample statistic.

In other words, the population mean of 68.3 years is a fixed value, and it does not change based on the sample mean or any other sample statistic. Therefore, we can simply state that the mean retirement age is 68.3 years, which is the given information provided in the question.

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The patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

To determine how many tablets the patient needs to take daily, we need to divide the total amount of the drug prescribed by the dose of each tablet.

Since the patient is prescribed 3 grams of the drug daily, we first need to convert this to milligrams (mg), as the tablets are available in milligram form.

1 gram = 1000 milligrams, so 3 grams = 3,000 milligrams

The pharmacist has 750 mg tablets available, so we can calculate the number of tablets the patient needs to take daily by dividing the prescribed dose by the dose of each tablet:

Number of tablets = Prescribed dose ÷ Dose per tablet

Number of tablets = 3,000 mg ÷ 750 mg

Number of tablets = 4

Therefore, the patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

Therefore, the patient will take 4 tablets daily.

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The distance between the intersection and the bank is equal to 77.0 feet.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

Note: Let the distance between the intersection and the bank be represented by the variable x.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

x/50 = 382/248

248x = 382(50)

x = 19,100/248

x = 77.0 feet.

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Complete Question:

The intersection of the two roads shown forms two similar triangles. If AC is 382 feet, MP is 248 feet, and the gas station is 50 feet from the intersection, how far from the intersection is the bank?

Answer: $1,652.

Step-by-step explanation:

To calculate Jen's net worth, we need to subtract her liabilities from her total assets:

Net worth = Total assets - Liabilities

In this case, Jen's total assets are $6,964, and her liabilities are $1,670 for credit card debt and $3,642 for a student loan. So:

Net worth = $6,964 - $1,670 - $3,642

Net worth = $1,652

Therefore, Jen's net worth is $1,652. Answer: $1,652.

Probability sampling procedures are instances where every unit in the population has a non-zero chance of being selected. (Option a)

Probability sampling is a type of sampling method used in statistical analysis, where each member of the population has a known and equal probability of being selected. This means that every possible unit in the population has a non-zero chance of being selected for the sample.

Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling. These methods are typically used when population parameters are unknown or when the researcher wants to make generalizations about the population based on the sample data.

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A box of chocolate on sale for 20% means that 80% of its original value remain.

Therefore, the sale price of the box of chocolate = $12 x 80% = $9.6

The sales price of box of chocolates is 9.6 dollars.

Given that, a $12 box of chocolate on sale for 20% off.

A sale price is the discounted price at which goods or services are being sold.

Here, sales price = Original price - 20% of Original price

= 12 - 20% of 12

= 12 - 20/100 ×12

= 12 - 0.2×12

= 12 - 2.4

= $9.6

Therefore, the sales price of box of chocolates is 9.6 dollars.

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Answer:

x = -13

Step-by-step explanation:

x+[tex]\frac{x+2}{3}[/tex]=-8

Step 1- You multiply both sides by 3
x + x + 2= -24
2x + 2 = -24

Step 2- You then minus 2 from both sides
2x = -26

Lastly, you divide both sides by 2
x = -13

And there you go!
Viola
Hope this helped

In the following question, A linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data is said to be True.

What is a linear system? In mathematics, a linear system refers to a system of linear equations that can be expressed in matrix form as Ax = b. A is a matrix, x is a vector, and b is a constant vector. When working with linear systems, we must keep track of the numerical accuracy of the computations. When a small change in the matrix or constant vector produces a large change in the solution, the matrix is said to be ill-conditioned.

The mathematical concept of condition numbers measures the sensitivity of a matrix to changes in the problem data. If a matrix has a high condition number, it is said to be ill-conditioned, whereas if it has a low condition number, it is said to be well-conditioned. An ill-conditioned matrix is difficult to solve numerically because a small error in the input data can produce a large error in the computed solution.

Therefore, the statement that "a linear system is ill-conditioned if its solution is highly sensitive to small changes in the problem data" is correct, and it is true.

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The polynomial (D) y = x4 + 2x3 – 3x2 – 2x + 1 has the graph that passes through the points (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329) respectively.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Variables are sometimes known as indeterminates in mathematics.

x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.

So, substitution and trial-and-error are the best ways to solve this problem given the various points and equations that are available as options.

In this regard, we change the equations' examples from 4 to x and see which one produces 89. The solution is D.

Therefore, the polynomial (D) y = x4 + 2x3 – 3x2 – 2x + 1 has the graph that passes through the points (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329) respectively.

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Complete question:

What polynomial has a graph that passes through the given points? (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329)

a)y = 2x3 – 3x2 – 2x + 1

b)y = 1x4 – 2x3 – 3x2 + 2x + 1

c)y = x4 – 2x3 + 3x2 + 2x – 1.

d)y = x4 + 2x3 – 3x2 – 2x + 1

The smallest positive integer y such that the product xy is a perfect cube is 3.

To find the value of y, we need to factorize x, which is 7 * 24 * 48.

We can then find the prime factorization of xy, which will help us determine the smallest integer y that will make the product a perfect cube.

Since 7, 24, and 48 are already factored, we can express x as:

x = 2⁴ * 3 * 7²

To make xy a perfect cube, we need to ensure that the exponents of all the prime factors are multiples of 3.

Therefore, we need to add a factor of 3 to the exponent of 2 in x to make it a multiple of 3. This gives us:

xy = 2⁷ * 3² * 7²

The smallest integer y that can make this product a perfect cube is 3, because we need to add a factor of 1 to the exponent of 2 in xy to make it a multiple of 3, and the smallest integer that can achieve this is 3.

Thus, the smallest positive integer y such that the product xy is a perfect cube is 3.


The question is: A number x is equal to [tex]$7\cdot24\cdot48$[/tex]. What is the smallest positive integer y such that the product xy is a perfect cube

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No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.

No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.

If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.

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There are 56 different health-care plans to choose from if one plan is selected from each category.

To calculate the total number of different health-care plans, we need to multiply the number of options in each category.

Number of basic health plans = 7

Number of dental plans = 4

Number of vision care plans = 2

Using the multiplication principle of counting, the total number of different health-care plans is:

7 x 4 x 2 = 56

Therefore, there are 56 different health-care plans to choose from if one plan is selected from each category.

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Answer:

Part A:

Assuming that Morgan kicks the ball at an angle that will allow it to clear the crossbar, we can use the following formula to determine how far she must kick the ball:

Distance = Height / tan(θ)

where θ is the angle at which the ball is kicked.

Since the field goal is 16 feet off the ground and we want the ball to clear the crossbar, we can assume that Morgan needs to kick the ball at an angle of approximately 45 degrees. Therefore, plugging in the given values, we get:

Distance = 16 / tan(45)

Simplifying the equation, we get:

Distance = 16 / 1

Therefore, Morgan must kick the ball a distance of 16 feet to make the extra point if she stands 30 feet from the field goal.

Part B:

To arrive at this conclusion, we used the formula for the distance of a projectile when given the initial velocity, angle, and height of the object. However, since we were not given the initial velocity, we assumed that Morgan would need to kick the ball at an angle of approximately 45 degrees to clear the crossbar. This is a common assumption in football, as it allows for the ball to travel the farthest distance possible while still clearing the crossbar. Additionally, we assumed that there was no wind or other external factors that could affect the trajectory of the ball. With these assumptions, we were able to determine that Morgan would need to kick the ball a distance of 16 feet to make the extra point if she stood 30 feet from the field goal.

The measure of angle ACD is approximately 109.5 degrees.

What are parallel lines ?

Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.

To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:

cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)

We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:

cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3

Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:

cos(ACD) = (-1/3) ≈ 109.5 degrees

Therefore, the measure of angle ACD is approximately 109.5 degrees.

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The point (2,2) may be considered an anomaly and should be investigated further to determine if it is a valid data point or if it should be excluded from the analysis.

The relation of the point (2,2) to the line of best fit can be determined by analyzing the residual value of this point. The residual value is the difference between the actual y-value and the predicted y-value based on the line of best fit. If the residual value is close to zero, then the point lies on the line of best fit. If the residual value is positive, then the actual y-value is higher than the predicted y-value, and if the residual value is negative, then the actual y-value is lower than the predicted y-value.

Unfortunately, the data necessary to determine the residual value of the point (2,2) is not provided in the question. Therefore, it is impossible to determine the exact relation of this point to the line of best fit.

However, we can make some generalizations based on the location of the point relative to the trend of the data.

If the point (2,2) lies close to the line of best fit, with a residual value close to zero, then it can be said that the point follows the trend of the data and is a typical data point. However, if the point lies far away from the line of best fit, with a large positive or negative residual value, then it can be said that the point is an outlier and does not follow the trend of the data.

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Increasing the sample size leads to a more accurate estimation of the population mean.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

As the sample size, n, increases, the center of the sampling distribution of sample means becomes more precise and closer to the true population mean. This is known as the central limit theorem, which states that as the sample size increases, the distribution of sample means becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In other words, as we take larger and larger samples, we are more likely to obtain sample means that are closer to the true population mean. This is because larger samples are less affected by random fluctuations and more likely to provide a representative picture of the population as a whole.

Therefore, increasing the sample size leads to a more accurate estimation of the population mean.

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Answer:

2023- answer is A-0

Step-by-step explanation:

Using the method of reduction of order, you can find a second solution to Problems 18-22.

In this method, we assume the second solution will have the same form as the first one, but with different constants of integration. To find the second solution, we substitute the first solution into the differential equation and solve for the remaining constant.

To illustrate, let's say Problem 18 is:

$$y''-2y'+y = 0$$

We start with a first solution of the form: $y_1=e^rx$.

Substituting this into the differential equation, we get:

$$r^2e^rx -2re^rx+e^rx=0$$

Rearranging and dividing by $e^rx$ yields:

$$r^2 -2r+1=0$$

Using the quadratic formula, we find two possible solutions for $r$:

$r=1$ and $r=-1$

Using these two values for $r$, we can write our two solutions as:

$y_1 = e^x$ and $y_2 = e^{-x}$

This same method can be applied to Problems 19-22 to find the second solution.

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The function f(x) = sec(x) has no x-intercepts.

The y-intercept of the graph of f(x) = sec(x) is (0, 1).

From the question, we are to identify any x-intercepts and y-intercepts of the graph of f(x) = sec(x).

The function f(x) = sec(x) is defined as the reciprocal of the cosine function, that is:

f(x) = 1 / cos(x)

The cosine function has a zero at x = π/2 + nπ, where n is an integer.

At these values of x, the denominator of the secant function becomes zero, and the function becomes undefined.

Therefore, the function f(x) = sec(x) has no x-intercepts.

To find the y-intercept, we need to evaluate the function at x = 0, which gives:

f(0) = 1 / cos(0) = 1 / 1 = 1

Hence, the y-intercept of the graph of f(x) = sec(x) is (0, 1).

The graph of the function f(x) = sec(x) is shown below.

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The correct option B. The expression for the inverse is f¹(x) = (x - 7)².

A one-to-one function is given. We have to write an expression for the inverse function.

Given function: f(x)=√x+7

The inverse of a function is found by switching the x and y coordinates and solving for y.

So, the expression for the inverse function will be:

f¹(x) = y = √x + 7 ... (1)

Replace x with y and simplify to isolate y from the radical.

   y = √x + 7

=> y - 7 = √x

=> (y - 7)² = x

Hence, the inverse of the given function is given byf¹(x) = (x - 7)².

So, the correct option is B) f¹(x)=(x-7)².

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a) The degree of freedom for a sample size 25 is equals to the 24 and the critical value t* for 80% confidence interval and degree of freedom 24 is equals to 1.318.

b) The degree of freedom for a sample size 55 is equals to the 54 and the critical value t* for 98% confidence interval and degree of freedom 54 is equals to 2.403.

The t-distribution has a bell-shaped density curve but has more variance (spread) than a normal bell curve.

Step 1: First express the confidence level as a number (in decimal) c with 0<c<1.

Step 2: Determine the significance level, denoted

α, by α = 1 − c.

Step 3: Use the t-distribution table to obtain the t-score (critical value) tα/2 where (i) the α is from Step 2 and (ii) the degrees of freedom equals n−1, where n is the sample size.

a) 80% of confidence interval and observation of

Sample size, n = 25

From above definition, degree of freedom= n - 1 = 25 - 1 = 24 and c = 80%

= 0.80

Significance level, α = 1- c = 1 - 0.80 = 0.20

and α/2 = 0.10 then use the t-table the critical t-value for this 80% confidence interval, t₀.₁₀ = 1.711.

b) 98% confidence interval with 55 observations. So, Sample size, n = 55

degree of freedom = n - 1 = 55 - 1 = 54,

c = 98% = 0.98

Significance level, α = 1-0.98 = 0.02

and α/2 = 0.01, then use the t-table the critical t-value for this 98% confidence interval, t₀.₀₁ = 2.669

Hence required value is 2.669.

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The given angles and measures is given below:

In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.

5) tan x = 153 / 41

x = tan^-1 ( 153 / 41 )

75 degrees

6) tan y = 25/25

y = tan^-1 ( 25/25 )

45 degrees

7) sin z = 10/28

z= sin^-1 ( 10/28 )

21 degrees

8) cos a = 47/50

a = cos^-1( 47/50)

20 degrees

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The transformation performed on f(x) = x² to create h(x) = 1/5f(x) is the graph is compressed horizontally by the factor 1/5

Transformations are mathematical operations performed on a graph or function to change the shape, size or orientation of the graph or function.

Given that we have the function f(x) = x² and it is transformed into the graph h(x) = 1/5f(x).

So, the graph is  compressed horizontally by the factor 1/5

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The net proceeds for Luis would be amount $1,169.50. This is calculated by subtracting the cost of the stock (100 x $6.35 = $635) and the commission (2% of $635 = $12.70) from the sale of the stock (100 x $12.57 = $1,257) and subtracting the flat fee of $15. ($1,257 - $635 - $12.70 - $15 = $1,169.50).

The net proceeds for Luis from the sale of the stock were calculated by subtracting the cost of the stock, the commission fee, and the flat fee from the proceeds of the sale. The cost of the stock was 100 shares at $6.35 per share, which totaled  amount $635. The commission fee was 2% of the cost of the stock, which was $12.70. The flat fee was a set fee of $15. The proceeds from the sale of the stock was 100 shares at $12.57 per share, which totaled $1,257. The net proceeds for Luis was calculated by subtracting the cost of the stock, the commission fee, and the flat fee from the proceeds of the sale, which was $1,257 - $635 - $12.70 - $15 = $1,169.50.

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2,364 ÷ 57 ≈ 41. Therefore, Hannah made 41 full bags of candy.

To solve this problem, we use integer division to find the number of full bags Hannah made. We divide the total number of candy pieces by the number of pieces in each bag and take the integer part of the result. This is because we are only interested in the number of full bags, not partial bags. In this case, we have 2,364 pieces of candy and each bag holds 57 pieces, so 2,364 ÷ 57 ≈ 41. This means that Hannah made 41 full bags of candy.

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The given statement "if we take a simple random sample from a normal distribution, the probability that the sample mean is equal to the population mean is 1 (i.e., 100%)" is false.

The probability that a sample mean is equal to the population mean is actually zero, since any given sample will differ slightly from the population mean due to sampling error. However, as the sample size increases, the sample mean is likely to be close to the population mean, and the probability of it being equal approaches 1 (i.e., 100%).

To explain further, the population mean is the mean of the entire population and is calculated by adding up all the values of the population and dividing them by the total number of individuals in the population. A sample mean, on the other hand, is the mean of a sample taken from the population and can be calculated by adding up the values of the sample and dividing them by the total number of individuals in the sample. Since the sample size is usually smaller than the population size, the sample mean is likely to be slightly different from the population mean due to sampling error.

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Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.

4. A scale factor is the ratio of the scales of an original object and a new object.

Scale factor = Ordinated dimension / original dimension

Scale factor = [tex]\frac{10}{15}[/tex]

Scale factor = [tex]\frac{2}{3}[/tex]  (or) 0.67

5. Length of EH

Scale factor = [tex]\frac{EH}{AD}[/tex]

[tex]\frac{EH}{AD}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{EH}{24} = \frac{2}{3}[/tex]

EH = 2 * 8

EH = 16 units

6. Length of AB

Scale factor = [tex]\frac{EF}{AB}[/tex]

[tex]\frac{EF}{AB}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{6}{AB} = \frac{2}{3}[/tex]

AB = 3 * 3

AB = 9 units.

Therefore, Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.

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Answer: B. 44°

if i'm wrong then its C