7(x+12)-4 algebraic expression

Answer:

x>= -46/9 (x greater than or equal to -46/9)

Step-by-step explanation:

when translating the question, at most means that it is less than or equal to the value being named, therefore the equation is 9x+21<= -25

to begin solving we subtract 21 from both sides and get 9x<=-46

then when we divide by 9 we have to flip the less than sign because we have to flip it if we multiply or divide.

This gives us the answer, x>=-46/9 which does not simplify any further

Answer:

The answer is the third one down

Step-by-step explanation:

l5-3xl = -8

Absolute value cannot equal a negative number.

Step-by-step explanation:

l5-3xl = -8

the | | is absolute value to it so it cant be negative number

Answer:

48

Step-by-step explanation:

Since 80 pupils is the total amount of pupils in Year 9...

5/5 = 80

1/5 = 80 ÷ 5 = 16

3/5 = 16 x 3 = 48 (The amount of pupils who said red is their favourite colour in Year 9)

The heights of married men are approximately normally distributed with a mean of 70 inches and a standard deviation of 2 inches, while the heights of married women are approximately normally distributed with a mean of 65 inches and a standard deviation of 3 inches. Consider the two variables to be independent. Determine the probability that a randomly selected married woman is taller than a randomly selected married man.

According to the problem statement, the two variables are independent. Therefore, we need to find the probability of P(Woman > Man).  We have the following information given: Mean height of married men = 70 inches Standard deviation of married men = 2 inches Mean height of married women = 65 inches Standard deviation of married women

= 3 inches We need to calculate the probability of a randomly selected married woman being taller than a randomly selected married man. To do this, we need to calculate the difference in their means and the standard deviation of the difference. \(μW - μM = 65 - 70 = -5σ2W - σ2M = 9 + 4 = 13σW - M = √13σW - M = √13/(√2)σW - M = 3.01\)Now, we can standardize the normal distribution using the formula,

(X - μ)/σ, where X is the value we want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution. \(P(Woman > Man) = P(Z > (W - M)/σW-M) = P(Z > (0 - (-5))/3.01) = P(Z > 1.66)\) Using the normal distribution table, we can find the probability of Z > 1.66 to be 0.0485. Therefore, the probability of a randomly selected married woman being taller than a randomly selected married man is 0.0485.

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Work Shown:

x³ + x² + x + 1

(x³ + x²) + (x + 1)

x²(x+1) + 1(x + 1)

(x² + 1)(x + 1)

The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.

The factored form of x³ + x² + x + 1 is (x²+1)(x+1).

A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.

We have,

x³ + x² + x + 1

Now, making groups as

(x³ + x²) + (x + 1)

= x² (x + 1) + (x+1)

= (x²+1)(x+1)

So, resulting expression is  (x²+1)(x+1).

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The probability that a randomly selected firm will earn between 9191 and 9797 million dollars is, 0.1879

We have to given that,

The mean income of firms in the industry for a year is 8585 million dollars with a standard deviation of 99 million dollars.

Hence, We need to standardize the values of 9191 and 9797 to a standard normal distribution with a mean of 0 and a standard deviation of 1. We can do this using the z-score formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For x = 9191:

z = (9191 - 8585) / 99 = 0.61

For x = 9797:

z = (9797 - 8585) / 99 = 1.22

Now, we need to find the probability that a randomly selected firm will have an income between 9191 and 9797 million dollars.

This is equivalent to finding the area under the standard normal distribution curve between z = 0.61 and z = 1.22.

We can use a standard normal distribution table or calculator to find this probability.

For example, using a standard normal distribution table, we can find that:

P(0.61 < Z < 1.22) = 0.1879

Therefore, the probability that a randomly selected firm will earn between 9191 and 9797 million dollars is, 0.1879 or 18.79%.

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Answer:

Step-by-step explanation:

So we know what a gradient is = y=mx+c So you have to make a triangle with the 2 numbers touching a line and make a triangle the conects to both of them. and then you will get the answer

True. depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception

The dequeue method of a LinkedQueue class throws a QueueUnderflowException when the queue is empty, and the user attempts to remove an element from it. This is because removing elements from an empty queue is not allowed and violates the basic properties of a queue data structure. Therefore, depending on the circumstances, the dequeue method may throw a QueueUnderflowException to indicate that the operation is invalid.

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Answer:

4

Step-by-step explanation:

The volume is length times width times Hight. so we already have 12 and three, so divide 144 by 12, then by 3, you will get 4.

The answer average speed is120KM/h

What is speed?

The speed of an object, also known as v in common parlance and kinematics, is the size of the change in position per unit of time or the size of the change in position over time; as such, it is a scalar quantity.The average speed of an object in a given period of time is equal to the distance travelled by the object divided by the length of the intervalthe instantaneous speed is the upper limit of the average speed as the length of Velocity and speed are different concepts.

Given in the question a car travels in 40Km/h

Total distance will be 's' = speed * time.

The total round trip avg speed is 60km/h

So time is taken to reach = s/40 hr

And time is taken to return back = s/x hr

The total time is given = 2s/60

We can write 2s/60 = s/40+s/x

⇒ 1/x = 1/30-1/40

⇒1/x = 1/120

⇒x = 120 KM/hour

Hence the, the average speed in the return journey is 120KM/hour.

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Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280.

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Given data ,

Let the principal amount be = A

The value of A = $ 1400

Let the rate of interest be = r

The value of r = 10 %

Let the number of years = T

The value of T = 2 years

Now , the simple interest is calculated by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Substituting the values in the equation , we get

Simple Interest = ( 1400 x 10 x 2 ) / 100

Simple Interest = 14 x 20

Simple Interest = $ 280

Therefore , the simple interest in 2 years is $ 280

And , the total amount Patrick has to give back to the bank is given by the formula

Amount in 2 years = Principal + Interest

Amount in 2 years = 1400 + 280

Amount in 2 years = $ 1680

Therefore , the amount in 2 years is $ 1680

Hence , Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280

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(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

If the coin is fair then there is a 1/2 chance of the coin landing on heads or tails . So the probability of 6 consecutive heads would be (1/2)6 = 1/64

Answer:

x = 300

Step-by-step explanation:

of means multiply and is means equals

25% * x = 75

Change to decimal form

.25x = 75

Divide each side by .25

.25x/.25 = 75/.25

x = 300

Answer:

300

Step-by-step explanation:

Assume the unknown value is 'Y'

75 = 25% x Y

75 = 25/100 x Y

Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:

Y = 3 x 100/25

Y = 300%

Answer: 75 is 25 percent of 300

Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.

In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.

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Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:

a

Step-by-step explanation:

PLEASE HELP 15 points

Usando un sistema de ecuaciones, se encuentra que

-----------------

-----------------

-----------------

Primero, encontramos la edad de Pedro, reemplazando la primera ecuación en la segunda

\(x + 6 = 2(y + 6)\)

\(y + 25 + 6 = 2y + 12\)

\(y + 31 = 2y + 12\)

\(2y - y = 31 - 12\)

\(y = 19\)

Pedro tiene 19 años.

-----------------

Quanto a Javier:

\(x = y + 25 = 19 + 25 = 44\)

Javier tiene 44 años.

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The inverse of the matrix [5 2; 7 3] is [3 -2; -7 5].To find the inverse of a matrix, we'll use the formula for a 2x2 matrix:

Inverse = 1 / (ad - bc) * [d -b]

                         [-c a]

The  2x2 matrix is:

[a b]

[c d]

Inverse = 1 / (ad - bc) * [d -b]

                         [-c a]

Let's calculate the inverse of the given matrix:

[5 2]

[7 3]

Here, `a = 5`, `b = 2`, `c = 7`, and `d = 3`.

The determinant of the matrix is given by `ad - bc`. So, `ad - bc = (5 * 3) - (2 * 7) = 15 - 14 = 1`.

Since the determinant is non-zero (1 ≠ 0), the matrix has an inverse.

Now, we can use the formula to find the inverse:

Inverse = 1 / (ad - bc) * [d -b]

                         [-c a]

Plugging in the values:

Inverse = 1 / 1 * [3 -2]

                [-7 5]

Therefore, the inverse of the matrix [5 2; 7 3] is:

[3 -2]

[-7 5]

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Answer:

y=-3/2x+4

slope=-3/2

y-int= 4

answer a)

soln,

or, 4x + 84 = 180° [being co-interrior angle]

or, 4x = 180 - 84

or, 4x = 96

or, x = 96/4

x = 24

answer b)

soln,

or, 2x + 5 = 135° [being corresponding angle]

or, 2x = 135 - 5

or,2x = 130

or, x = 130/2

x = 65°

Step-by-step explanation:

well if it's helpful mark me as brainlest please

Answer:

$0.59

Step-by-step explanation:

We first find the unit rate of the large water bottles after the promotion. To do this we divide 6.3 by 3 to get 2.1. Then we want to subtract 2.69 by 2.1 to get our final answer, $0.59.

Answer:

-1/2

Step-by-step explanation:

It’s y2 - y1 over x2-x1

- 2 - 3

— - -—-

6 - (-4)

= -5/10

= -1/2

Answer: 1/2

Step-by-step explanation:

Answer:

turning it I think.........

The given series is convergent. To determine whether the series is convergent or divergent, we need to examine the behavior of its terms as n approaches infinity. The given series is a sum of two terms: 1/9 and e^(-n).

The term 1/9 is a constant term that does not depend on n. The series ∑(1/9) is a geometric series with a common ratio of 1, which is less than 1. Therefore, this series converges, and its sum can be found using the formula for the sum of a geometric series:

Sum = a / (1 - r),

where a is the first term and r is the common ratio. In this case, a = 1/9 and r = 1, so the sum of the series ∑(1/9) is given by:

Sum = (1/9) / (1 - 1) = (1/9) / 0.

However, dividing by zero is undefined, so the sum of the series ∑(1/9) is not defined.

The second term in the series is e^(-n), where e is Euler's number. As n approaches infinity, e^(-n) approaches 0. This term contributes to the convergence of the series. Therefore, the series ∑(1/9 + e^(-n)) is convergent. However, since the first term does not have a defined sum, we cannot determine the sum of the series.

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If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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The given function is f(x), and the second derivative of the function is f′′(x) = 10x2sin(x). The formula for calculating the derivative of f(x) with respect to x isf'(x) = d/dx f(x).

Similarly, the formula for the second derivative is f′′(x) = d/dx f′(x).Here, f(0) = 4 and f′(0) = 2 is given. To calculate the value of f(2), follow these steps: Solving the second derivative equation. The second derivative equation is f′′(x) = 10x2sin(x)Integrating with respect to x on both sides, we have f′(x) = ∫f′′(x) dx = ∫10x2sin(x) dx

Let u = x2, and dv = sin(x) dx∴du/dx = 2xdv/dx = sin(x)∴v = ∫sin(x) dx = – cos(x)

Therefore, f′(x) = uv – ∫vdu= – x2cos(x) – ∫– cos(x).2x dx= – x2cos(x) + 2∫x cos(x) dx= – x2cos(x) + 2[x sin(x) + cos(x)] + C

Here, C is the constant of integration.

Calculate the value of f(x) by integrating f′(x) with respect to x∫f′(x) dx = ∫[– x2cos(x) + 2(x sin(x) + cos(x))] dx= – ∫x2cos(x) dx + 2∫x sin(x) dx + 2∫cos(x) dx= x2sin(x) + 2x cos(x) – 2 sin(x) + C1

Here, C1 is the constant of integration.

Substituting f(0) = 4 in the above equation, we have C1 = 4 – 2 = 2

Thus, the function becomesf(x) = x2sin(x) + 2x cos(x) – 2 sin(x) + 2

Given that f′(0) = 2, substituting x = 0, we get f′(0) = 0 * sin(0) + 2 * cos(0) – 2 * sin(0) + 2= 2

Hence, f(2) = 4sin(2) + 4cos(2) – 2sin(2) + 2= 2sin(2) + 4cos(2) + 2Ans: 2sin(2) + 4cos(2) + 2
To find the value of the function f(x) at x=2, we need to first integrate the second derivative, f^''(x), twice.

f^''(x) = 10x² * sin(x)

Integrating the first time:

f^'(x) = ∫(10x² * sin(x)) dx

This integral is quite complex and cannot be solved analytically using elementary functions. Instead, we will use the given information about f(0) and f^'(0) to approximate f(2).

We know that f^'(0) = 2, and since sin(0) = 0, the contribution from the integral at x=0 is zero. Therefore, the constant of integration for f^'(x) is 2.

f^'(x) = ∫(10x^2 * sin(x)) dx + 2

Now, integrate f^'(x) to find f(x):

f(x) = ∫(∫(10x^2 * sin(x)) dx + 2) dx

Again, this integral is too complex to solve analytically using elementary functions. However, we know that f(0) = 4, and since sin(0) = 0, the contribution from the integral at x=0 is zero. Therefore, the constant of integration for f(x) is 4.

f(x) = ∫(∫(10x² * sin(x)) dx + 2) dx + 4

Given the complexity of the integral, it is not possible to find an exact value for f(2). Instead, numerical methods such as Simpson's rule or a Taylor series approximation can be used to estimate the value of f(2).

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A factor of the polynomial function is (d) x + 4

The solution of the cubic function f(x) are given as:

−4, 5/3, and 1.

This means that:

x = -4, x = 5/3 and x = 1

Set the above equations to 0

x + 4 = 0, x - 5/3 = 0 and x - 1 = 0

From the list of options, we have

(d) x + 4

Hence, a factor of the polynomial function is (d) x + 4

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