(-3,-2). (9. -15)
Slope

Answer:

x+6=±5

Step-by-step explanation:

Step-by-step explanation:

The answer is 60°

because

360÷6 = 60

Answer:

  see below

Step-by-step explanation:

There are some subtleties here.

Drawing conclusions

When conclusions are drawn based on patterns, it is called inductive reasoning. When those conclusions are drawn based on facts, it is called deductive reasoning.

Theories and proofs

When a pattern is observed, it gives rise to a conjecture. If there is a counterexample, then the conjecture must be declared false. If an argument can be made based on logic, then the conjecture is said to have a proof. A proven conjecture (statement) can then be referred to as a theorem.

Answer: I have no clue lol but if I had to guess I'd say A because it just seems like it stands out from the rest

Step-by-step explanation:

the maximum constant speed is not determined by the car's speed, but rather by the requirement that the normal force must be greater than or equal to the gravitational force.

To determine the maximum constant speed at which the 2-mg car can travel over the crest of the hill without leaving the surface of the road, we can consider the forces acting on the car at that point.

At the crest of the hill, the car experiences two main forces: the gravitational force acting downward and the normal force exerted by the road surface upward. For the car to remain on the road, the normal force must be equal to or greater than the gravitational force.

The gravitational force acting on the car can be calculated as:

\(F_{\text{gravity}} = m \cdot g\)

where:

\(m\) = mass of the car (2 mg)

\(g\) = acceleration due to gravity (approximately 9.8 m/s²)

So, \(F_{\text{gravity}} = 2 mg \cdot g = 2 \cdot 2 \cdot g = 4g\)

The normal force acting on the car at the crest of the hill should be at least equal to \(4g\) for the car to remain on the road.

Now, let's consider the centripetal force acting on the car as it moves in a circular path at the crest of the hill. This centripetal force is provided by the frictional force between the car's tires and the road surface. The maximum frictional force can be calculated using the equation:

\(F_{\text{friction}} = \mu_s \cdot F_{\text{normal}}\)

where:

\(\mu_s\) = coefficient of static friction between the car's tires and the road surface

\(F_{\text{normal}}\) = normal force

For the car to remain on the road, the maximum static frictional force must be equal to or greater than \(F_{\text{gravity}}\).

So, we have:

\(F_{\text{friction}} \geq F_{\text{gravity}}\)

\(\mu_s \cdot F_{\text{normal}} \geq 4g\)

Substituting \(F_{\text{normal}}\) with \(4g\):

\(\mu_s \cdot 4g \geq 4g\)

The \(g\) terms cancel out:

\(\mu_s \geq 1\)

Since the coefficient of static friction (\(\mu_s\)) can have a maximum value of 1, it means that the maximum constant speed at which the car can travel over the crest of the hill without leaving the surface of the road is when the static friction is at its maximum.

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Answer:

\(x=-1,\frac{5}{7}\)

Step-by-step explanation:

1) Split the second term in \(7{x}^{2}+2x-5\) into two terms.

1 - Multiply the coefficient of the first term by the constant term.

\(7\times -5=-35\)

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

\(7x^2+7x-5x-5\)

2)  Factor out common terms in the first two terms, then in the last two terms.

\(7x(x+1)-5(x+1)=0\)

3) Factor out the common term x+1.

\((x+1)(7x-5)=0\)

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

\(x=-1,\frac{5}{7}\)

\(\huge\text{Hey there!}\)

\(\huge\textbf{What are the quadratic formulas?}\)

\(\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\)

\(\bullet\rm{\ ax^2 + bx + c = 0}\)

\(\huge\textbf{What are we solving for?}\)

\(\rm{7x^2 + 2x - 5 = 0}\)

\(\huge\textbf{What do we have to do?}\)

\(\rm{7x^2 + 2x - 5 = 0}\)

\(\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}\)

\(\rm{(7x - 5)(x + 1) = 0}\)

\(\rm{(7x - 5) \times (x + 1) = 0}\)

\(\huge\textbf{Set 0 to the factors:}\)

\(\rm{7x - 5 = 0\ or\ x + 1 = 0}\)

\(\huge\textbf{Simplify it:}\)

\(\rm{x = \dfrac{5}{7}\ or\ x = -1}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The 10th percentile is 22 and the 75th percentile is 46 for the given set of weights.

To find the 10th and 75th percentiles for the given set of weights, we first need to arrange the weights in ascending order:

21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 40, 42, 44, 46, 47, 48, 49, 50

Finding the 10th percentile:

The 10th percentile is the value below which 10% of the data falls. To calculate the 10th percentile, we multiply 10% (0.1) by the total number of data points, which is 20, and round up to the nearest whole number:

10th percentile = 0.1 * 20 = 2

The 10th percentile corresponds to the second value in the sorted list, which is 22.

Finding the 75th percentile:

The 75th percentile is the value below which 75% of the data falls. To calculate the 75th percentile, we multiply 75% (0.75) by the total number of data points, which is 20, and round up to the nearest whole number:

75th percentile = 0.75 * 20 = 15

The 75th percentile corresponds to the fifteenth value in the sorted list, which is 46.

Therefore, the 10th percentile is 22 and the 75th percentile is 46 for the given set of weights.

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Reason:

We have two pairs of congruent sides, and a pair of congruent angles between those sides. The tickmarks tell us which sides are congruent to one another.

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Answer:

2 3/4 feet

Step-by-step explanation:

Longwei should first recognize that implementing goals, policies, and structure is only one aspect of effective leadership. A leader's ability to motivate and inspire their employees is just as important. Therefore, Longwei should use the principles of organizational behavior (OB) to better understand his employees and their motivations.

Additionally, Longwei should take a personality assessment to become more self-aware of his own leadership style and how it may be impacting the employees. He should examine his perceptions and biases to ensure that he is making fair and objective judgments and decisions. This may involve seeking feedback from other leaders or mentors, participating in leadership development programs, or engaging in self-reflection and mindfulness practices.

By taking these steps, Longwei can better understand and address the unmotivated employees in his company. He can then develop strategies to engage and inspire them, such as offering incentives, providing opportunities for professional development, or creating a more positive and inclusive work environment. Ultimately, Longwei's success as a leader will depend not only on his ability to set and implement goals but also on his ability to motivate and engage his employees.

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Answer:

point H is in quadrant II

The appropriate symbols to use for the answer are: µ - z * (s / √n) < δ < µ + z * (s / √n)

To construct a confidence interval estimate for the mean body temperature of all healthy humans, we can use the symbol "µ" to represent the population mean.

A 99% confidence interval estimate for the mean body temperature can be represented as:

µ - z * (s / √n) < µ < µ + z * (s / √n)

In this expression:

"z" represents the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 99%).

"s" represents the sample standard deviation.

"n" represents the sample size.

Therefore, the appropriate symbols to use for the answer are:

µ - z * (s / √n) < δ < µ + z * (s / √n)

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Percentage of bags that weigh more than 9.25 ounces is 19.3%.

Given:

Mean μ = 9.12

standard deviation σ = 0.15

z = x - μ / σ

= 9.25 - 9.12 / 0.15

= 0.13/0.15

= 0.867

P(x>Z)  = 0.193

= 0.193/100

= 19.3%

Therefore Percentage of bags that weigh more than 9.25 ounces is 19.3%.

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Answer:

x = 19

y = 10

Step-by-step explanation:

3x - 5y - 7 = 0

x = 2k - 1

y = k

3x - 5y = 7

x = 2y - 1

3 * (2y - 1) - 5y = 7

6y - 3 - 5y = 7

6y - 5y = 10

y = 10

x = 2 * 10 - 1

x = 19

Answer:

1

Step-by-step explanation:

Answer:

x=4

y=-1

Step-by-step explanation:

x + 2y = 2

-x + y = -5

3y = -3

y = -1

If you would then plug in -1 (for y) then you would get x=4

For example:

x + 2(-1) = 2

x - 2 = 2

x = 4

OR

-x - 1 = -5

-1 + 5 = x

4 = x

x = 4

Answer: B

Step-by-step explanation:

To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.

Equation 1: y=2|x+6|-4

Equation 2: y=6

Now, we can substitute.

2|x+6|-4=6

Let's solve for x.

2|x+6|-4=6        [add both sides by 4]

2|x+6|=10          [divide both sides by 2]

|x+6|=5              [subtract both sides by 6]

x=-1

Now that we know x=-1 is one of the solutions, we can eliminate C and D.

We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.

|x+6|=-5              [subtract both sides by 6]

x=-11

Therefore, we know that B is the correct answer.

The value is 350.

From the question, we have

Dan uses the equation g(x)=5x+50 to model the balance of his savings account after saving for x weeks.

g(x)=5x+50

substituting the value x = 60, we get

g(60)=5*60+50

=300+50

=350

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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The value of this stock, assuming a required return of 10.50%, is approximately $81.90. None of the given options match this value.

To compute the value of the stock, we can use the dividend discount model (DDM) formula. The DDM formula states that the value of a stock is equal to the present value of its future dividends.
Using the formula, we can calculate the present value of the dividends as follows:
PV(dividends) = D1 / (1 + r) + D2 / (1 + r)^2
where D1 is the dividend to be paid next year, D2 is the dividend to be paid in two years, r is the required return.
Given:
D1 = $6.69
D2 = $7.02
r = 10.50% or 0.105

Plugging in these values into the formula:
PV(dividends) = $6.69 / (1 + 0.105) + $7.02 / (1 + 0.105)^2
PV(dividends) = $6.05 + $6.11
PV(dividends) = $12.16
Finally, to compute the value of the stock, we add the present value of the dividends to the future target price of the stock in two years:
Value of stock = PV(dividends) + Future target price
Value of stock = $12.16 + $69.74
Value of stock = $81.90
Therefore, the value of this stock, assuming a required return of 10.50%, is approximately $81.90. None of the given options match this value.

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The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer:

126

Step-by-step explanation:

The area of the top triangle is (6)(6)/2 = 18 square meters.

The area of the bottom rectangle is (9)(12)=108 square meters.

Adding these, we get the total area to be 126 square meters.

The most factorized form of the expression p^3+6p^2-4p is (p + 8)(p - 2).

Given an algebraic expression p³ + 6p² - 4p. we have to factorize it into its most factorized form. So, to factorize the given expression, we have to first take common p from all the terms:

p(p² + 6p - 4)

Now, we have to factorize the quadratic expression p² + 6p - 4.

To factorize the quadratic expression, we can either use the factorization method, splitting the middle term method, or the quadratic formula. But, to make the calculations simpler, we'll use the splitting of the middle term method.

For the quadratic expression p² + 6p - 4, the product of the coefficient of the square term and the constant term

= p² × (-4)

= -4p².

Now, we need to find two numbers such that their product is -4p² and their sum is 6p. It's easy to find that the two numbers are 8p and -2p.

We have to find two numbers whose product is -4p² and sum is 6p. On observing the coefficient of the square term, we can see that the only way we can get -4p² is by multiplying -4 with p².

So, we have to consider factors of -4 and pair them up so that their product is -4p². Similarly, to get the coefficient of the linear term, we have to add these factors of -4p².

So, we can write the quadratic expression as:p² + 8p - 2p - 4=> p(p + 8) - 2(p + 2)We can factorize this quadratic expression as:

p² + 6p - 4=> p(p + 8) - 2(p + 2)

Therefore, the given algebraic expression can be factorized as:p³ + 6p² - 4p=> p(p + 8) - 2(p + 2)

The most factorized form of the given expression is:

p(p + 8) - 2(p + 2)= p(p + 8) - 2 × 1 × (p + 2)

We can write this expression in two terms as:p(p + 8) - 2(p + 2)= (p + 8)(p - 2).

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The solutions of the given equation are 2 or -2

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, x²+2 = 6

x²+2 = 6

Solving we get,

x²+2 = 6

x² = 6-2

x² = 4

x = ±2

Hence, there are two solutions of the equation 2 or -2

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The expression that is equivalent to \((\frac{m-4}{m^4})/ m^2\) is the expression \(\frac{m-4}{(m^4)(m^2)}\)

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the expression:

\((\frac{m-4}{m^4})/ m^2\\\\This\ can\ be\ simplified\ to:\\\\(\frac{m-4}{m^4})*\frac{1}{m^2} \\\\=\frac{m-4}{(m^4)(m^2)}\)

The expression that is equivalent to \((\frac{m-4}{m^4})/ m^2\) is the expression \(\frac{m-4}{(m^4)(m^2)}\)

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Answer:

A

or M-4 / ( M + 4 ) ( M + 2 )

StartFraction m minus 4 Over (m + 4) (m + 2) EndFraction

Step-by-step explanation:

The probability that Suspect A is the guilty party is 2/3.

Suppose a crime is committed by one of the two suspects A and B. Initially, there is equal evidence against both of them. Further, in the investigation, it is found that the guilty party had a blood type found in 10% of the population. Suspect A does match this blood type, whereas the blood type of Suspect B is unknown.The probability that A is the guilty party is calculated as follows:

Let P(A) be the probability that A is guilty, and P(B) be the probability that B is guilty.As there is an equal amount of evidence against both suspects, both P(A) and P(B) are equal and can be expressed as P(A) = P(B) = 1/2.Let the probability of the blood type of a guilty party be X.

Since Suspect A's blood type matches the guilty party's blood type, the probability that he is the guilty party is P(X | A) = 1.Since Suspect B's blood type is unknown, we must take into account the possibility of him being the guilty party despite not matching the guilty party's blood type.

As a result, the probability that he is the guilty party is P(X | B) = 0.1.

The probability that the guilty party has blood type X can be expressed as:P(X)

= P(A) P(X | A) + P(B) P(X | B)P(X) = 1/2 × 1 + 1/2 × 0.1P(X) = 0.55

Using Bayes' theorem, we can calculate the probability that Suspect A is the guilty party:

P(A | X) = P(X | A) P(A) / P(X)P(A | X) = 1 × 1/2 / 0.55P(A | X) = 0.9091 ≈ 2/3.

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The main task for members during the final session is to put into words what has transpired from the first to the final session.

The group's goals should be discussed during the first few meetings, then each member's personal goals should be covered. Even small toddlers can follow and take part in these dialogues. They must be aware that the emphasis will be on defining and exploring particular issues and themes.

Over the years, I've discovered that assisting customers in comprehending what will occur during their initial meeting (often referred to as the "intake session") can be extremely beneficial in putting them at ease and beginning our partnership on a cordial and inviting note.

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