Let f(x)= (x+3)^2/x^2-9. Find a) lim x→-3 f(x), b) lim x→0 f(x), and c) lim x→3 f(x).

The true statement about the sampling distribution is "the sampling distribution of a statistic is a distribution that we should approximate in exercise by taking many small samples."

The sampling distribution is the theoretical distribution of a statistic (including the imply, median, or variance) based totally on all viable samples of a given size that could be taken from a population. it is a beneficial idea in statistics as it allows us to make inferences approximately the populace based on records gathered from a pattern.

In practice, we can not examine the whole sampling distribution, as it's far based totally on all viable samples, which isn't always feasible to gain. but, we will approximate the sampling distribution by taking many small samples from the population and calculating the applicable statistic for every sample.

Because the variety of samples increases, the distribution of these data will converge to the sampling distribution, allowing us to make more accurate inferences approximately the population.

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Answer:

$8.33 per soccer ball.

Step-by-step explanation:

Y max is =236.67   is the max profit from the soccer balls. This goes on when you charge 8.33 a ball

Answer:

need to solve the equation 150 = -6x2 + 100x - 180. I can subtract 150 from both sides and use the quadratic formula to find x = 4.53 and 12.13. This means that if the store sells soccer balls for $4.53 or $12.13, it will earn a daily profit of $150.

(1 + z^(2n))* is equal to (1 - z^(2n)) or its square. Hence, z^n/(1 + z^(2n)) can be converted to a real number, Therefore, z^n/(1 + z^(2n)) is a real number.

Given that n ∈ N and z ∈ C with |z| = 1 and z^(2n) ≠ -1, we need to prove that z^n/(1 + z^(2n)) ∈ R.

Let's take the conjugate of the denominator 1 + z^(2n). We know that for any complex number a + bi, its conjugate is given by a - bi.

Now, the conjugate of 1 + z^(2n) is 1 - z^(2n), and this is true for all values of z as z has magnitude 1.

Thus, (1 + z^(2n)) + (1 - z^(2n)) = 2 is real.

Also, z^n is a complex number as z is a complex number. Let's write z^n as cos(nx) + isin(nx), where x is some real number.

Now, z^n/(1 + z^(2n)) = (cos(nx) + isin(nx))/2, hence it is a complex number.

Dividing by a real number will convert the result into a real number. We can obtain a real number by taking the conjugate of the denominator (1 + z^(2n)) and multiplying the numerator and the denominator with it, because (1 + z^(2n))(1 - z^(2n)) = 1 - z^(4n). Let's call this C.

Let's take the conjugate of C, which is C* = (1 + z^(2n))* (1 - z^(2n))* = (1 - z^(2n))(1 - z^(2n)*).

Now, z^(2n) + z^(2n)* = 2cos(2nx), which is a real number.

So, C* = (1 - z^(2n))(1 - z^(2n)* ) = (1 - z^(2n))(1 - z^(2n)) = (1 - z^(2n))^2 is a non-negative real number, as the square of a real number is non-negative.

Thus, (1 + z^(2n))* is equal to (1 - z^(2n)) or its square. Hence, z^n/(1 + z^(2n)) can be converted to a real number.

Therefore, z^n/(1 + z^(2n)) is a real number.

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Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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ANSWER

Length of the playing alley = 9m

Width of the playing alley = 3m

STEP-BY-STEP EXPLANATION:

Given information

The perimeter of a rectangular playing alley = 24 m

The length of the alley is three times the width

Let l represents the length of the alley

Let w represents the width of the alley

Step 1: Write the formula for calculating the perimeter of a rectangle

Where l is the length and w is the width of the rectangle

Recall, length = 3 times the width of the alley

Mathematically,

Step 2: Substitute the value of l = 3w into the above formula

Step 3: Solve for w

From the calculations above, you will see that the width of the playing alley is 3m

Step 4: Solve for l

Hence, the length of the playing alley is 9m

Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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According to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

The natural logarithm, often denoted as ln(x), is a mathematical function that represents the logarithm to the base e, where e is the mathematical constant approximately equal to 2.71828.

To find out how long it will take for 300 grams of Mercury 203 to decay, we can use the exponential decay model.

The general formula for exponential decay is given by:

A(t) = A₀ * e^(-rt),

where A(t) represents the amount of the substance at time t, A₀ is the initial amount, r is the decay rate, and e is the base of the natural logarithm.

In this case, we have the initial amount A₀ = 300 grams and the decay rate r = 0.01481 (1.481% written as a decimal).

We want to find the time t when the amount A(t) is equal to zero. Substituting these values into the formula, we have:

0 = 300 * e^(-0.01481t).

To solve for t, we can divide both sides of the equation by 300 and take the natural logarithm of both sides:

ln(0) = ln(e^(-0.01481t)),

0 = -0.01481t.

To isolate t, we divide both sides by -0.01481:

0 / -0.01481 = t,

t = 0.

Therefore, according to the model, it will take 0 days for 300 grams of Mercury 203 to completely decay.

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Answer:

145° 7' 12"

Step-by-step explanation:

145.12° written in DMS form

145°

0.12 *60 (1 degree = 60 minutes)=7.2 minutes

0.2*60 ( 1 minute=60 sec)=0.2*60=12"

The standard deviation measures the spread or dispersion of a dataset. By calculating the standard deviation for both Class #1 and Class #2, it is determined that Class #2 has a larger standard deviation than Class #1.

We must calculate the standard deviation for both classes and compare the results to determine which class would likely have the larger age standard deviation. The spread or dispersion of a dataset is measured by the standard deviation.

Using Excel, let's determine the standard deviation for the two classes:

Class #1: 28, 19, 21, 23, 19, 24, 19, 20

Step 1: Determine the ages' mean (average):

Step 2: The mean is equal to 22.5 (28 - 19 - 21 - 23 - 19 - 24 - 19 - 20). For each age, calculate the squared difference from the mean:

(28 - 22.5)^2 = 30.25

(19 - 22.5)^2 = 12.25

(21 - 22.5)^2 = 2.25

(23 - 22.5)^2 = 0.25

(19 - 22.5)^2 = 12.25

(24 - 22.5)^2 = 2.25

(19 - 22.5)^2 = 12.25

(20 - 22.5)^2 = 6.25

Step 3: Sum the squared differences and divide by the number of ages to determine the variance:

The variance is equal to 10.9375 times 8 (32.25 times 12.25 times 2.25 times 12.25 times 6.25). To get the standard deviation, take the square root of the variance:

The standard deviation for Class #2 can be calculated as follows: Standard Deviation = (10.9375) 3.307 18, 23, 20, 18, 49, 21, 25, 19

Step 1: Determine the ages' mean (average):

Mean = (23.875) / 8 = (18 + 23 + 20 + 18 + 49 + 21 + 25 + 19) Step 2: For each age, calculate the squared difference from the mean:

(18 - 23.875)^2 ≈ 34.816

(23 - 23.875)^2 ≈ 0.756

(20 - 23.875)^2 ≈ 14.616

(18 - 23.875)^2 ≈ 34.816

(49 - 23.875)^2 ≈ 640.641

(21 - 23.875)^2 ≈ 8.316

(25 - 23.875)^2 ≈ 1.316

(19 - 23.875)^2 ≈ 22.816

Step 3: Sum the squared differences and divide by the number of ages to determine the variance:

Variance is equal to (34.816, 0.756, 14.616, 34.816, 640.641, 8.316, 1.316, and 22.816) / 8  99.084. To get the standard deviation, take the square root of the variance:

According to the calculations, Class #2 has a standard deviation that is approximately 9.953 higher than that of Class #1 (approximately 3.307).

The standard deviation estimates how much the ages in each class go amiss from the mean. When compared to Class 1, a higher standard deviation indicates that the ages in Class #2 are more dispersed or varied. That is to say, whereas the ages in Class #1 are somewhat closer to the mean, those in Class #2 have a wider range and are more dispersed from the average age.

This could imply that Class #2 has a wider age range, possibly including outliers like the student who is 49 years old, which contributes to the higher standard deviation. On the other hand, Class #1 has ages that are more closely related to the mean and have a smaller standard deviation.

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Thus, with 95% confidence that at least 90% of the values in a normal distribution fall within the tolerance interval of mean +/- 0.10.

We can use a standard normal distribution table to find the critical values, which is the z-score that corresponds to the given confidence level. For a 95% confidence level, the critical value is 1.96.

Next, we need to find the standard deviation of the normal distribution. We can use the formula:
tolerance interval = mean +/- z * (standard deviation / sqrt(n))

where mean is the mean of the distribution, z is the critical value, standard deviation is the standard deviation of the distribution, and n is the sample size. Since we don't have a sample size, we can assume a large sample size and use the population standard deviation instead.

Assuming a population standard deviation of 1, the tolerance interval is:
tolerance interval = mean +/- 1.96 * (1 / √(n))

To capture at least 90% of the values, we need to set the tolerance interval to be equal to 90%.
0.90 = 1.96 * (1 / √(n))

Solving for n, we get:
n = (1.96 / 0.10)^2
n = 384.16

Since we assumed a large sample size, we can round up to the nearest integer, which gives us a sample size of 385.

The tolerance interval for capturing at least 90% of the values in a normal distribution with a confidence level of 95% and a sample size of 385 is:
tolerance interval = mean +/- 1.96 * (1 / √t(385))

This can be simplified to:
tolerance interval = mean +/- 0.10

Therefore, we can say with 95% confidence that at least 90% of the values in a normal distribution fall within the tolerance interval of mean +/- 0.10.

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Answer:

C is the correct answer

Answer:

Yes dentro as options out not is me viking one produtions

\(14 \frac{4}{9}\) inches of ribbon will be left over.

Creating equal groupings or determining how many people go into each group after a fair distribution is the basic objective of division. Multiply the first percentage by the equivalent of the other to equal the quadratic formula. They factor everything and search for common traits after rewriting the partition as multiple of the first statement by the opposite of the latter.

Selena has a 130-inch-long ribbon in her possession.

If she strives to make 9-inch bracelets,

ribbon will be left over = 130/9

= \(14 \frac{4}{9}\)

In the end, Selena will have  \(14 \frac{4}{9}\) a ribbon left with her.

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Answer:

3rd choice

Step-by-step explanation:

Answer:

B. False

Step-by-step explanation:

5x² - 6x + 4 | 5 × 4 = 20

Can't factor it normally

           √b² - 4ac

 -b  ±   ---------------

                2a

           √(-6)² - 4(5)(4)

 -(-6)  ±   ---------------

                   2(5)

           √36 - 80

 6  ±   ---------------

                 10

    6 ± √-44

  ---------------

         10

    6 ± √-4 × 11

  ---------------

         10

    6 ± 2i√11

  ---------------

         10

The answer is actually

    3 ± i√11

  ---------------

         5

I hope this helps!

Answer:

  B.  False

Step-by-step explanation:

You want to know if (x -2) is a factor of 5x² -6x +4.

There are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:

  5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12

The value is not 0, so (x -2) is not a factor.

Another way to tell is to determine what the other factor would be.

The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...

  (5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial

The polynomial 5x² -6x +4 does not have a factor (x -2).

The graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.

Answer:

Multiplying Integers can be used in the real world in a lot of ways because of their positive and negative. The Positive and Negative will be used as like what you have to owe in money/cash or what you have.

Step-by-step explanation:

Hopes This Helps

The height of the flagpole is 27 feet.

Given,

If two triangles are similar, sides of these triangles will be proportional.

Height of the flagpole  = h feet

Shadow castes by the flagpole  = 72 feet

Height of the person  = 6 feet

Shadow casted by the person = 16 feet

By using the property of similar triangles,

Hence, h/6 = 72/16

h = (6×72)/ 16

h = 27 feet

Therefore, The height of the flagpole is 27 feet.

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Answer:

24 x 2.5 = 60...

Step-by-step explanation:

sorry if this is wrong...

have a good day

Answer:

1/6

Step-by-step explanation:

Each roll is independent.  So the probability of rolling a six is 1/6, regardless of the previous rolls.

The expression which is equivalent to the given expression is -7.74x² - 7.2x.

The given expression is (4.3x + 4)(−1.8x).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Now, the given expression can be solved as follows:

(4.3x + 4)(−1.8x)

Using distributive property

4.3x × (−1.8x) + 4 × (−1.8x)

= -7.74x² - 7.2x

Therefore, the expression which is equivalent to the given expression is -7.74x² - 7.2x.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Answer:

3

Step-by-step explanation:

ignore this i need more letters lol have a good day

Answer:

You could buy 3 cantaloupes.

Step-by-step explanation:

So, you have $6. Now, what we would do is (O is 1 cantaloupe):

If O cost $2, do the following:

O O O O O

2  2  2  2 2

Now, lets count up til we get 6:

2 + 2 = 4; 4 + 2 = 6;

After you have done that step, count how many 2's you see in that equation. I see 3.

Therefore, you could buy 3 cantaloupes.

Answer:

1. 3a2

Step-by-step explanation:

Answer:

1953.125

Step-by-step explanation:

(12.5)³

= 12.5 × 12.5 × 12.5

= 1953.125

Answer: 1953.125

(12.5)³

so 12.5 multiplied to itself thrice

12.5x12.5x12.5

which is 1953.125

the area of a circle with a rectangle will be [π w²2]/4.

What is the area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

area of the circle will be πr².

The area of a circle inscribed in a rectangle if the length of the rectangle is l and the width is w

= [π w²2]/4.

Hence the area of a circle with a rectangle will be [π w²2]/4.

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Answer:

fourth

Step-by-step explanation:

Angle X is the inscribed angle of the two arcs that measure 122 and 64 so

\(x = \frac{1}{2} (122 + 64)\)

\(x = \frac{1}{2} (186) = 93\)

A cyclic quadrilateral states that the opposite angles add up to 180

so

\(y = 18 0 - 83 = 97\)

The correct answer is the fourth option

Answer:

I think the answer is A reflection across the line y=1 and A reflection across the y-axis and then a translation 2 units to the right

Step-by-step explanation:

I’m not sure if this is the answer but I want to help out as much as possible

Answer:b

Step-by-step explanation:

When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer:

\(f( - 1) = - 1\)

Step-by-step explanation:

\(f(x) = {x}^{2} + 2x\)

Substitute x = -1 in the equation.

\(f( - 1) = {( - 1)}^{2} + 2( - 1) \\ f( - 1) = 1 - 2 \\ f( - 1) = - 1\)