Solve \frac{x^{2}-6 x+9}{2 x^{3}+19 x^{2}+40 x-25}<0 and show your answer on a number line.

Answer:

1. 8.75

2. 3.48

Step-by-step explanation:

hope this helps :3

Answer:

1. B $8.75

2. D Between 3 and 4 cups/ 4.11

Answer:

Use the sum of functions definition:

In our case both f and g are represented by k, so the sum of functions is:

Substitute the function values to get:

This is matching the answer choice D

Answer:

5(4) - 6 + 5(4) - 6

Step-by-step explanation:

\(\textsf{Given}:\quad k(x)=5x-6\)

\(\begin{aligned}(k+k)(x) & =k(x)+k(x)\\\\\implies (k+k)(4) & =k(4)+k(4)\\& = \left[5(4)-6\right]+\left[5(4)-6\right]\\& = 5(4)-6+5(4)-6\end{aligned}\)

47.5% between 38 and 52 requests for new lightbulbs have been made.

Given,

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs.

The mean of the distribution, μ = 52

Standard deviation, σ = 7

We have to find the  approximate percentage of lightbulb replacement requests numbering between 38 and 52 using empirical rule;

Here,

z score corresponding to 38 and 52

z score = (x - μ) / σ = (38 - 52) / 7 = -2

Now,

z score corresponding to 52

z score = 52 -52 / 7 = 0/7 = 0

We are aware that, in accordance with the empirical rule, 68% of the data are within one standard deviation of the mean and 95% are within two.

By comparing the z-scores of data point 38 and 52, we can observe that data point 38 is at the mean. 38 is therefore -2 standard deviations above the mean. That is -2σ to 2σ

The center of the normal distribution curve is known to be the mean. Therefore, we will divide 95% by 2 to obtain the percentage of data points 2 SD above the mean.

95/2 = 47.5%

As a result, 47.5% between 38 and 52 requests for new lightbulbs have been made.

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Answer:

Step-by-step explanation:

its not

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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1. The height of the cone is equal to

2. You can solve for the slant height, s by applying Pythagorean's theorem.

3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

8792 =  1/3 × 3.14 × 20² × h

26,376 =  3.14 × 400 × h

Height, h = 26,376/1,256

Height, h = 21 mm.

Question 2.

In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.

Question 3.

By applying Pythagorean's theorem, we have the following:

r² + h² = s²

20² + 21² = s²

400 + 441 = s²

s² = 841

Slant height, s = √841

Slant height, s = 29 mm.

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By following the histogram which represents the number of pages in each book within a collection. The frequency of books containing at least 250 but fewer than 300 pages is 7.

The correct answer is option C.

Let's determine the histogram and calculate the frequency of books containing at least 250 but fewer than 300 pages.

Assuming the histogram, let's consider the following ranges and frequencies:

Number of Pages (Range) Frequency

100 - 149 4

150 - 199 8

200 - 249 12

250 - 299 9

300 - 349 5

To find the frequency of books containing at least 250 but fewer than 300 pages, we need to sum up the frequencies of the corresponding range, which is "250 - 299".

According to the given histogram, the frequency of books within the range "250 - 299" is 9.

Therefore, the correct answer is: c) 7

According to the provided histogram, there are 9 books within the collection that contain at least 250 but fewer than 300 pages.

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The data points are within the Control limits, indicating that the candy production process is operating consistently and without any significant issues that would require intervention or adjustment.

The process is in control or out of control, we can utilize control charts and statistical methods. In this case, we will use a control chart called the X-Bar chart, which is used to monitor the process mean over time.

1. Calculate the control limits:

  - First, we need to calculate the upper control limit (UCL) and lower control limit (LCL) for the X-Bar chart. The formula for the control limits is:

    UCL = mean + (3 * standard deviation)

    LCL = mean - (3 * standard deviation)

    Given:

    Mean = 16.8 grams

    Standard deviation = 0.7 grams

    UCL = 16.8 + (3 * 0.7) = 18.9 grams

    LCL = 16.8 - (3 * 0.7) = 14.7 grams

2. Plot the data points:

  - Plot the readings on the X-Bar chart using the given data points: 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 18.4.

3. Analyze the chart:

  - Examine the plotted data points to see if they fall within the control limits. If a data point falls outside the control limits, it suggests that the process may be out of control.

  In this case, we observe that all the data points fall within the control limits of 14.7 grams (LCL) and 18.9 grams (UCL). None of the points exceed these limits.

4. Conclusion:

  - Since all the data points fall within the control limits, we can conclude that the process is in control. There is no evidence of any special causes of variation present in the data.

the data points are within the control limits, indicating that the candy production process is operating consistently and without any significant issues that would require intervention or adjustment.

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Effective leadership can be demonstrated in many different ways, but here are a few examples of actions that may indicate effective leadership by a group leader:

1. Clear communication: A group leader who communicates clearly and effectively with their team is more likely to build trust and respect among the group.

2. Empathy and emotional intelligence: A leader who demonstrates empathy and emotional intelligence can help build a positive team culture by understanding and acknowledging the feelings and needs of their team members.

3. Delegation and empowerment: An effective leader knows how to delegate tasks and responsibilities to team members in a way that maximizes their strengths and abilities, while also providing support and guidance as needed.

4. Leading by example: A leader who sets a positive example for their team by modeling the behaviors and attitudes they want to see in their team is more likely to earn respect and trust from their team members.

5. Strategic thinking: A leader who is able to think strategically and make informed decisions based on data and evidence can help steer their team towards success.

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The probability of an offspring pea having a green pod is p = 0.75.Using the Binomial Distribution formula, we get: Mean, μ = np

= 5 x 0.75

= 3.75 Standard deviation,

σ = √(npq)

= √(5 x 0.75 x 0.25)

= √0.9375

= 0.9682.

Therefore, the mean number of peas with green pods is 3.75 and the standard deviation is 0.9682 when groups of 5 offspring peas are generated, assuming a 0.75 probability that an offspring pea has a green pod. Probability theory is used to model and analyze random phenomena. The Binomial Distribution is one of the most common probability distribution functions that we use when dealing with a situation in which there are only two outcomes, such as tossing a coin, rolling a die, or selecting an item from a box. In this question, we have to find the mean and standard deviation of the number of peas with green pods when groups of 5 offspring peas are generated, and there is a 0.75 probability that an offspring pea has a green pod.

Using the Binomial Distribution formula, we get: Mean, μ = np Standard deviation, σ = √(npq) Where, n is the total number of trials (5),p is the probability of success (0.75), and q is the probability of failure (1 - p = 0.25).Mean, μ = np

= 5 x 0.75 = 3.75 Standard deviation,

σ = √(npq)

= √(5 x 0.75 x 0.25)

= √0.9375

= 0.9682 Therefore, the mean number of peas with green pods is 3.75 and the standard deviation is 0.9682 when groups of 5 offspring peas are generated, assuming a 0.75 probability that an offspring pea has a green pod. The mean tells us the average number of peas with green pods that we can expect to get when generating groups of 5 offspring peas. The standard deviation tells us how much the actual number of peas with green pods can vary from the mean.

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Answer:

using the pythagoras theorem

Step-by-step explanation:

\( \sqrt{4 {}^{2} - ( \sqrt{7}) {}^{2} } = 3\)

Step-by-step explanation:

cosine is cos(angle)= adjacent/hypotenuse

sine is sin(angle) = opposite/hypotenuse

Tangent is tan(angle)= opposite/adjacent

for all of those

if the equation is something like tan(69)= x/69

multiply both sides by 69 so it will end up as x=69tan(69) and put that in the calculator

if it is something like tan(69)= 69/x

just swap x and tan(69)

it is much easier

it will then be 69/tan(69) and put that in the calculator

The weighted average cost of capital WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

To calculate the cost of capital for Brozierz Ltd, we need to calculate the cost of each component of their capital structure and weight them according to their proportion in the overall capital structure.

First, let's calculate the cost of equity using the Capital Asset Pricing Model (CAPM):

Cost of equity = risk-free rate + beta x (return on market - risk-free rate)

= 0.06 + 1.4 x (0.15 - 0.06)

= 0.165 or 16.5%

Next, let's calculate the cost of preference shares:

Cost of preference shares = (fixed dividend rate / market price of preference shares) + flotation costs

= (0.1 x 3 / 2.5) + 0

= 0.12 or 12%

The cost of debt is simply the interest rate on the bank loan, which is 12% per annum.

Now, we can calculate the weighted average cost of capital (WACC) using the formula:

WACC = (proportion of equity x cost of equity) + (proportion of preference shares x cost of preference shares) + (proportion of debt x cost of debt) x (1 - tax rate)

Let's calculate the proportion of each component:

Proportion of equity = 300,000 x 2.40 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.375

Proportion of preference shares = 100,000 x 2.50 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.125

Proportion of debt = 500,000 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.5

Therefore, the WACC is:

WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

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Zack should use a line with one arrowhead to map an abandoned line of reasoning.

A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.

The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.

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Answer:

Show that if \(f(a) = f(b) = 0\) for some \(a,\, b \in [-2,\, 2]\) where \(a \ne b\), then by Rolle's Theorem \(f^{\prime}(x) = 0\) for some \(x \in (-2,\, 2)\). However, no such \(x\) exists since \(f^{\prime}(x) < 0\) for all \(x \in (-2,\, 2)\!\).

Note that Rolle's Theorem alone does not give the exact value of the root. Neither does this theorem guarantee that a root exists in this interval.

Step-by-step explanation:

The function \(f(x) = x^{3} - 12\, x + 11\) is continuous and differentiable over \([-2,\, 2]\). By Rolle's Theorem. if \(f(a) = f(b)\) for some \(a,\, b \in [2,\, -2]\) where \(a \ne b\), then there would exist \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\).

Assume by contradiction \(f(x)\) does have more than one roots over \([-2,\, 2]\). Let \(a\) and \(b\) be (two of the) roots, such that \(a \ne b\). Notice that \(f(a) = 0 = f(b)\) just as Rolle's Theorem requires. Thus- by Rolle's Theorem- there would exist \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\).

However, no such \(x \in (a,\, b)\) could exist. Notice that \(f^{\prime}(x) = 3\, x^{2} - 12\), which is a parabola opening upwards. The only zeros of \(f^{\prime}(x)\) are \(x = (-2)\) and \(x = 2\).

However, neither \(x = (-2)\) nor \(x = 2\) are included in the open interval \((-2,\, 2)\). Additionally, \(a,\, b \in [-2,\, 2]\), meaning that \((a,\, b)\) is a subset of the open interval \((-2,\, 2)\). Thus, neither zero would be in the subset \((a,\, b)\). In other words, there is no \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\). Contradiction.

Hence, \(f(x) = x^{3} - 12\, x + 11\) has at most one root over the interval \([-2,\, 2]\).

Write this out as an equation, let the unknown number be X:

4 + 4x = 6x

Subtract 4x from both sides:

4 = 2x

Divide both sides by 2:

2 = x

Rewrite:

X = 2

The number is 2

Equatiοn C will prοvide the sοlutiοn based οn the inputs prοvided.

y - 1 =3(x - 2).

An infinitely small lοcatiοn knοwn as a pοint is sοmething that has lοcatiοn but nο spatial expanse. A pοint is a nοn - dimensiοnal οbject, in οther wοrds! An illustratiοn fοr this wοuld be the meeting οf twο lines. It has neither a width nοr a length nοr a height.

Given: A line with a slοpe οf 3 and the specified pοint (2, 1).

Tο determine: What is a line's pοint-slοpe shape.

We stated that slοpe equals 3 pοints (2, 1).

Accοrding tο the pοint-slοpe fοrmula, given a pοint\((x1 - y1)\) with a slope of m, the line's equation can be expressed as  \(y - y1 = m(x - x1).\)

Here \((x1 - y1) = ( 2, 1)\)

Then Equation of line y - 1 = 3(x - 2).

Therefore, Equation C. y - 1 = 3(x - 2).

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If A girl is 5 cm taller than her mother and 8 cm less than her dad, the height of the girl's dad is 122 cm.

Let's assume that the height of the girl's mother is x cm. Then, according to the given information, the height of the girl would be (x + 5) cm and the height of her dad would be (x + 5 + 8) cm or (x + 13) cm.

Now, we know that the total height of the three individuals is 3.45 m or 345 cm (since 1 m = 100 cm). Therefore, we can write an equation as follows:

x + (x + 5) + (x + 13) = 345

Simplifying the equation, we get:

3x + 18 = 345

Subtracting 18 from both sides, we get:

3x = 327

Dividing both sides by 3, we get:

x = 109

Therefore, the height of the girl's mother is 109 cm, the height of the girl is (109 + 5) cm or 114 cm, and the height of the girl's dad is (109 + 13) cm or 122 cm.

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9514 1404 393

Answer:

Step-by-step explanation:

The ratio of perimeters is the ratio of corresponding sides.

  first : second = 8 : 6 = 4 : 3 . . . ratio of perimeters

The ratio of areas is the square of the ratio of linear dimensions.

  first : second = 4² : 3² = 16 : 9 . . . ratio of areas

Answer:

look at the explanation <33

Step-by-step explanation:

The first figure is similar to the second figure. The ratio would be 4:3

Answer:

1 4 3 4 4 = ilyvm

1 4 3 3 = ilyt

Step-by-step explanation:

\( \huge \bold{answer}\)

A and B because x is smaller than y and both A and B show that

The inequality |x| ≤ |y| and |y| ≥ |x| is true.

Option A and Option B are true.

Given,

x = -2

y = 8

We need to see which inequality is true.

We have,

< - less than

> - greater than

≤ - less than and equal to

≥ - greater than and equal to

The modulus of a number x is given by |x|

|x| = x

|-x| = x

Find which satisfy x = -2 and y = 8.

|x| ≤ |y|

|-2| ≤ |8|

2 ≤ 8

This is true.

|y| ≥ |x|

|8| ≥ |-2|

8 ≥ 2

This is true

|x| > |y|

|-2| > |8|

2 > 8

This is not true.

|y| < |x|

|8| < |-2|

8 < 2

This is not true.

Thus the inequality |x| ≤ |y| and |y| ≥ |x| is true.

Option A and Option B are true.

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Step-by-step explanation:

if we put the amount of hours and how much Justin has been paid into a ratio we will get this:

$318.75 : 25 hours

in order to find out how much he has been paid for just one hour of work we must divide both sides by 25.

this is because 25 hours / 25 = 1 hour. let's try that:

$318.75 / 25 = $12.75

and 25 hours / 25 = 1 hour

let's put these values back into our ratio:

$12.75 : 1 hour

as you can see we have worked out the total amount Justin made in 1 hour of work, aka how much he earned in an hour.

if you need any more help, just ask :D

Answer: The perimeter of the flower box can be determined by adding up the lengths of all four sides. In this case, we can see that the width of the flower box is represented by the variable x in feet, and the height is given as 2(x+4). To find the perimeter, we need to add up the lengths of the top and bottom (2x) and the left and right sides (2(x+4)). So, the perimeter P(x) can be expressed as:

P(x) = 2x + 2(x+4)

Simplifying this expression:

P(x) = 2x + 2x + 8

P(x) = 4x + 8

So the perimeter of the flower box is 4x+8 feet, based on the width x in feet.

Step-by-step explanation:

The vector parametrization for the equation of line passing through points (2,5,3) and (6,9,6) is: r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K).

WE know that parameterization of the a curve is provided by each vector-valued function.

Since the pair of equations x = x (t) and y = y (t) that express the coordinates of a point along a curve in terms of such a parameter is known as a parameterization of a curve.

Given passing points:

(2,5,3) and (6,9,6)

In vector form;

Let vector a = 2i + 5j + 3k

Let vector b = 6i + 9j + 6K

Let μ be any constant.

Then, using the vector parametrization:

The equation of line in vector form for the given points is;

r(t)= a + μb

r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K)

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Correct question:

Find the vector parametrization for equation of the line that passes through the points (2,5,3) and (6,9,6). (Give your answer in the form 〈∗,∗,∗〉. Express numbers in exact form. Use symbolic notation and fractions where needed.)

r(t)=?

The speed of a car on a New York tollway during rush hour traffic is a continuous random variable.

The speed of a car on a New York tollway during rush hour traffic is a continuous random variable. This is because the speed can take on any value within a given range and is not limited to specific, separate values like a discrete random variable would be.

A random variable is a mathematical concept used in probability theory and statistics to represent a numerical quantity that can take on different values based on the outcomes of a random event or experiment.

Random variables can be classified into two types: discrete random variables and continuous random variables.

Discrete random variables are those that take on a countable number of distinct values, such as the number of heads in multiple coin flips.

Continuous random variables are those that can take on any value within a certain range or interval, such as the weight or height of a person.

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