3(4x-7)=27
What does x =?
Please help asap im timed!!!

The equation for the plane tangent to the surface at the point (0, 6, 9) is 6y - z = 27.

To find the equation for the plane tangent to the surface defined by the parametric equations x = u, y = u^2 + 2v, z = v^2, at the specified point (0, 6, 9), we need to determine the normal vector to the tangent plane.

The normal vector can be obtained by taking the cross product of the partial derivatives of the surface equations with respect to the parameters u and v at the given point.

Let's find the partial derivatives first:

∂x/∂u = 1

∂x/∂v = 0

∂y/∂u = 2u

∂y/∂v = 2

∂z/∂u = 0

∂z/∂v = 2v

Evaluating the partial derivatives at the point (0, 6, 9):

∂x/∂u = 1

∂x/∂v = 0

∂y/∂u = 0

∂y/∂v = 2

∂z/∂u = 0

∂z/∂v = 12

Taking the cross product of the partial derivatives:

N = (∂y/∂u * ∂z/∂v - ∂z/∂u * ∂y/∂v, ∂z/∂u * ∂x/∂v - ∂x/∂u * ∂z/∂v, ∂x/∂u * ∂y/∂v - ∂y/∂u * ∂x/∂v)

= (0 * 12 - 0 * 2, 0 * 0 - 1 * 12, 1 * 2 - 0 * 0)

= (0, -12, 2)

Therefore, the normal vector to the tangent plane is N = (0, -12, 2).

Now, we can write the equation for the tangent plane using the point-normal form of a plane:

0(x - 0) - 12(y - 6) + 2(z - 9) = 0

Simplifying:

-12y + 72 + 2z - 18 = 0

-12y + 2z + 54 = 0

-12y + 2z = -54

Dividing by -2 to simplify the coefficients:

6y - z = 27

So, the equation for the plane tangent to the surface at the point (0, 6, 9) is 6y - z = 27.

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The volume of five volleyballs is 26310.15 cubic cm if the volleyball has a surface area of 1465 square cm.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

We know the surface area of the sphere is given by:

SA = 4πr²

1465 = 4πr²

r = 10.79 cm

Volume of the sphere = 4πr³/3

V = 4π(10.79)³/3

V = 5262.03 cubic cm

Volume of five volleyballs = 5×5262.03 = 26310.15 cubic cm

Thus, the volume of five volleyballs is 26310.15 cubic cm if the volleyball has a surface area of 1465 square cm.

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9514 1404 393

Answer:

  C  18(2 + 3)

Step-by-step explanation:

The GCD of 36 and 54 is their difference, 18. Factoring that out of the sum, you have ...

  36 + 54 = (18·2 + 18·3) = 18(2 + 3) . . . . matches choice C

The two solutions to the equation -6 sec (θ) - 3 = -15 on the Interval [0°, 360°) are θ = 60° and θ = 300°.

The equation -6 sec (θ) - 3 = -15 on the interval [0°, 360°), we will isolate the variable θ.

Let's begin by rearranging the equation:

-6 sec(θ) - 3 = -15

Next, we'll add 3 to both sides of the equation:

-6 sec(θ) = -12

Now, we'll divide both sides of the equation by -6:

sec(θ) = 2

To solve for θ, we need to find the angle whose secant is 2. The secant function represents the reciprocal of the cosine function. In the interval [0°, 360°), the cosine function is positive in the first and fourth quadrants.

In the first quadrant (0° to 90°), we have cos(θ) = 1/sec(θ) = 1/2, which does not hold true.

In the fourth quadrant (270° to 360°), we also have cos(θ) = 1/sec(θ) = 1/2, which is true.

Therefore, one solution to the equation is in the fourth quadrant. We can find this angle by taking the inverse cosine (arccos) of 1/2:

θ = arccos(1/2)

Using a calculator, we find:

θ ≈ 60°

So, one solution to the equation is θ = 60°.

To find the second solution, we can use the symmetry property of the cosine function. Since cos(θ) = cos(360° - θ), we can find the second solution by subtracting the first solution from 360°:

θ = 360° - 60°

θ = 300°

Therefore, the two solutions to the equation -6 sec (θ) - 3 = -15 on the interval [0°, 360°) are θ = 60° and θ = 300°.

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Answer:

60 dollars per hour.

Step-by-step explanation:

Hope this helps.

By evaluating a cost equation, we will see that Sam needs to pay $4.17

We know that one pound of chocolate costs $6.95, then we have the cost equation:

y = $6.95*x

Where y is the cost and x is the number of pounds of chocolate that you want to buy.

So, if you want to buy 0.6 of a pound, then we have x = 0.6

Then we can evaluate the equation to get:

y = $6.95*0.6

y = $4.17

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Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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Step-by-step explanation:

4 ( 100 -3)   =  4 x 100  -  4 x 3

                    = 400 - 12 = 388

The average weight of the colony over the interval [1,4] is 47.83 newtons

The average value of a function is found by taking the integral of the function over the interval and dividing by the length of the interval.

Given,

\(w(t)=12.5e^{0.5t}\)

The average value of the given function

\(w_{avg} =\frac{1}{b-a}\int\limits^a_b {w(t)} \, dt\)

Here the interval is [1,4]

Therefore, a=1 and b= 4.

Substitute the values of w(t),a and b in the equation

\(w_{avg}= \frac{1}{4-1}\int\limits^4_1 {12.5e^{0.5t} } \, dx \\w_{avg}= \frac{1}{3}\int\limits^4_1 {\frac{25e^{0.5t} }{2} } \, dx\)

Consider,

\(u=\frac{t}{2}\\ \frac{du}{dt}=\frac{1}{2}\\dt=2du\)

Then,

\(w_{avg}= \frac{25}{3}\int\limits^4_1 {e^{u} } \, du\\ w_{avg}= \frac{25}{3}[e^{4/2}-e^{1/2}]\\ w_{avg}= \frac{25}{3}[e^{2}-\sqrt{e}]\\ w_{avg}= \frac{25}{3}[5.74]\\ w_{avg}=47.83\)

Hence, the average weight of the colony over the interval [1,4] is 47.83 newtons

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Answer:

\(y=\frac{1}{4}x+4\)

Step-by-step explanation:

ind the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )

to find the line parallel to  x + 4y = 28 .

Answer:

x=9.4

Step-by-step explanation:

x intercept is the point where the graph crosses the x axis and y always =0

-2.65x+25=0

-2.65x=-25

x=-25/-2.65

x=500/53

x=9.4

Given: Differential equation of the form: \($\frac{dx}{dt}+ax=b$\)

This is a first-order, linear, ordinary differential equation with a constant coefficient. To solve this differential equation we need to follow the steps below:

First, find the homogeneous solution of the differential equation by setting \($b=0$.$\frac{dx}{dt}+ax=0$\)

Integrating factor, \($I=e^{\int a dt}=e^{at}$\)

Multiplying both sides of the differential equation by \($I$.$\frac{d}{dt}(xe^{at})=0$\)

Integrating both sides.\($xe^{at}=c_1$\)

Where \($c_1$\) is a constant.

Substituting the initial condition,\($x(0)=x_0$.$x=e^{-at}c_1$\)

Next, we need to find the particular solution of the differential equation with the constant \($b$.\)

In the present case, \($b=constant$\)

Therefore, the particular solution of the differential equation is also a constant.

Let this constant be \($c_2$.\)

Then, \($\frac{dx}{dt}+ax=b$ $\implies \frac{dc_2}{dt}+ac_2=b$ $\implies c_2=\frac{b}{a}$\)

Thus, the general solution of the differential equation is,\($x(t)=e^{-at}c_1+\frac{b}{a}$\)

Where\($c_1$\) is the constant obtained from the initial condition,

and \($e$\)is the exponential constant.

If the initial condition is \($x(t_0)=x_0$ then,$x(t)=e^{-a(t-t_0)}c_1+\frac{b}{a}$\)

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Once all layers are solved, the Rubik's cube is done.

The Rubik's cube is a classic puzzle that has been challenging people for decades. It consists of a 3x3x3 cube with each of the six faces covered in smaller colored cubes, or "cubies".

There are many different methods for solving the Rubik's cube, but the most popular method is called the "layer-by-layer" method.

The first step in solving the Rubik's cube is to solve the top layer. This is done by aligning the top layer cubies with the center cubies of the same color. Once the top layer is solved, the next step is to solve the middle layer.

Finally, the last step is to solve the bottom layer. This is done by aligning the bottom layer cubies with the center cubies of the same color.

It's important to memorize some basic algorithms and techniques to be able to solve the cube efficiently, these techniques can vary from simple moves to more complex ones. There are many resources available online to learn these techniques, such as video tutorials and written guides.

Solving the Rubik's cube can be a fun and rewarding challenge, and it can also help to improve your problem-solving skills and spatial reasoning.

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Using the arrangement formula, it is found that there are \(28! = 3.05 \times 10^{29}\) possible seating arrangements.

The number of possible arrangements of n elements is given by the arrangement formula, as follows:

\(A_n = n!\)

In this problem, 28 students are arranged on 28 desks, hence \(n = 28\), and:

\(A_{28} = 28! = 3.05 \times 10^{29}\)

Hence, there are \(28! = 3.05 \times 10^{29}\) possible seating arrangements.

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Answer:

wouldn't it be -3 * 8 = -24

Step-by-step explanation:

also I love your pfp

Answer:

8

Step-by-step explanation:

-24/-3 = 8

The derivative of y = f(x) + g(x) is y' = 8x + 1 / (2√x).

(a) To find the derivative of the function f(x) = 4x^2 using first principles, we start by taking the limit as h approaches 0 of the difference quotient:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

Substituting f(x) = 4x^2 into the equation, we have:

f'(x) = lim(h->0) [(4(x + h)^2 - 4x^2) / h]

Expanding and simplifying the numerator:

f'(x) = lim(h->0) [(4(x^2 + 2xh + h^2) - 4x^2) / h]

= lim(h->0) [(4x^2 + 8xh + 4h^2 - 4x^2) / h]

= lim(h->0) (8x + 4h)

= 8x

Therefore, the derivative of f(x) = 4x^2 is f'(x) = 8x.

(b) To find the derivative of the function g(x) = √x + 3 using first principles, we again use the difference quotient:

g'(x) = lim(h->0) [g(x + h) - g(x)] / h

Substituting g(x) = √x + 3 into the equation:

g'(x) = lim(h->0) [√(x + h) + 3 - (√x + 3)] / h

= lim(h->0) [√(x + h) - √x] / h

To simplify the expression, we multiply the numerator and denominator by the conjugate of the numerator (√(x + h) + √x):

g'(x) = lim(h->0) [(√(x + h) - √x)(√(x + h) + √x)] / (h(√(x + h) + √x))

= lim(h->0) [(x + h) - x] / (h(√(x + h) + √x))

= lim(h->0) h / (h(√(x + h) + √x))

= lim(h->0) 1 / (√(x + h) + √x)

= 1 / (2√x)

Therefore, the derivative of g(x) = √x + 3 is g'(x) = 1 / (2√x).

(c) To find the derivative of y = f(x) + g(x), we can apply the sum rule of differentiation. Since we know the derivatives of f(x) and g(x) from parts (a) and (b) respectively, the derivative of y with respect to x is:

y' = f'(x) + g'(x)

= 8x + 1 / (2√x)

Hence, the derivative of y = f(x) + g(x) is y' = 8x + 1 / (2√x).

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Answer: Add 40 to both sides to collect like terms on each side of the equation

Step-by-step explanation: That's the first step

Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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The algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

The H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.

The two terms x³y⁴ and x⁴y⁴ of the algebraic expression x³y⁴ - x⁴y⁴ have their highest common factor to be x³y⁴ such that:

x³y⁴ × 1 = x³y⁴

x³y⁴ × x = x⁴y⁴

and

x³y⁴ - x⁴y⁴ = x³y⁴ × 1 - x³y⁴ × x

x³y⁴ - x⁴y⁴ = x³y⁴(1 - x)

Therefore, the algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

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The probability that the sample proportion (the proportion living in the dormitories) is at least 0.70 is approximately 0.02. This is option A

Let p be the sample proportion living in the dormitories.The mean of the sample proportion is given by:μp = p = 0.60.

The standard deviation of the sample proportion is given by:σp = sqrt(p(1-p)/n)=sqrt(0.6*0.4/80)= 0.049.The sample size n = 80.

From Chebyshev' s theorem: P(|X - μ| ≥ k.σ) ≤ 1/k².

Substituting μ.p = 0.60 and σ.p = 0.049, we have:P(|p - 0.60| ≥ k*0.049) ≤ 1/k².

The question asks us to find the probability that the sample proportion (the proportion living in the dormitories) is at least 0.70.

So, we have:p ≥ 0.70 = 0.60 + k*0.049, k = (0.70 - 0.60)/0.049 = 2.04

.Substituting k = 2.04 in the above expression, we have:

P(|p - 0.60| ≥ 2.04*0.049) ≤ 1/(2.04)²= 0.2362.

So, P(p ≥ 0.70) = P(p - 0.60 ≥ 0.10)= P(p - 0.60/0.049 ≥ 2.04)= P(Z ≥ 2.04)≈ 0.0207.

Hence, the probability that the sample proportion (the proportion living in the dormitories) is at least 0.70 is approximately 0.02.

So, the correct answer is A

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The probability that the document will reach its destination through service B, given that it has already reached its destination through service A, is 0.8.

The conditional probability we are looking for is P(B | A) where B is the document reaching its destination through service B and A is the document reaching its destination through service A.

P(B | A) = P(A and B) / P(A)

We know that the document has already reached its destination through service A,

therefore P(A) = 1.

The probability that it will also reach its destination through service B is the conditional probability P(B | A).

Therefore, P(B | A) = P(A and B) / P(A) can be simplified to P(B | A) = P(A ∩ B) / P(A)

where P(A ∩ B) is the probability that the document reaches its destination through both service A and service B.

Let's assume that the probability of the document reaching its destination through service A is 0.9 and the probability of the document reaching its destination through service B is 0.8.

The probability of the document reaching its destination through both services A and B is the product of the probabilities P(A) and P(B) which is 0.9 x 0.8

= 0.72.

Substituting these values in the equation P(B | A) = P(A ∩ B) / P(A) gives us:

P(B | A) = 0.72 / 0.9 = 0.8

Therefore, the probability that the document will reach its destination through service B,

given that it has already reached its destination through service A, is 0.8.

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Step-by-step explanation:

to subtract mixed numbers:

example 5 1 /4 - 7 1/2

you change the denominator to the GCM so it would be 4 so you would have now 5 1/4 - 4 1/4 then you do 5-4 which is 1 and 1/4- 1/4 is 0 so it just would be 1

Answer:

x² + 7x + 10 = 0

Subtract 10 from both sides

x² + 7x = -10

Use half the x coefficent (7/2) as the complete the square term

(x + 7/2)² = -10 + (7/2)²

   note: the number added to "complete the square" is (7/2)² = 49/4

(x + 7/2)² = -10 + 49/4

(x + 7/2)² = 9/4

Take the square root of both sides

x + 7/2 = ±3/2

Subtract 7/2 from both sides

x = -7/2 ± 3/2

x = {-5, -2}

Answer:

The area is 36m^2

Step-by-step explanation:

6×6=36

Answer:

6 x 6 = 12

Step-by-step explanation:

area is length x width and all sides on a square are congruent ( so all of the sides are 6)

According to the computations, project Z has the highest NPV of $1,671.13 million, and it is the most appropriate investment for Delta Corporation.

Delta Corporation should invest in Project Z, which is expected to generate the highest cash flows over a 10-year period with the highest NPV at the 15 percent required rate of return.

The Net Present Value (NPV) technique is a capital budgeting method that measures the present value of future cash flows that a project will generate. NPV calculates the present value of future cash flows by discounting them back to their current value. It is a cash flow method that recognizes the time value of money.

Projects X, Y, and Z have initial outlays of $800 million, $850 million, and $930 million, respectively. The projects are expected to generate free cash flows after taxes of $252 million for project X, $250 million for project Y, and $290 million for project Z each year.

Each project has a depreciable life of ten years. The required rate of return is 15 percent.

Using the Net Present Value (NPV) technique, we can compute the most appropriate investment for Delta Corporation. Here's the computation:

Project X

NPV = $252 million x [1- (1/1.15)^10] / 0.15NPV = $1,508.97 million

Project Y

NPV = $250 million x [1- (1/1.15)^10] / 0.15NPV = $1,468.57 million

Project ZNPV = $290 million x [1- (1/1.15)^10] / 0.15NPV = $1,671.13 million

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The most appropriate investment for Delta Corporation is Project X, and they should proceed with it since it has the highest NPV of $35.45 million.

Net present value (NPV) is a tool used in capital budgeting to assess the profitability of a potential investment or project. It is calculated by subtracting the present value of cash outflows from the present value of cash inflows. If the resulting NPV is positive, it is recommended to proceed with the investment. On the other hand, if the NPV is negative, it is recommended to reject the investment.

The NPV formula is as follows:

\(NPV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + ... + CFn / (1 + r)n - Initial Investment\)

Where:

CF = Cash flow

r = Required rate of return

n = Number of periods

Let's evaluate three projects: Project X, Project Y, and Project Z.

For Project X:

Year 0: -800 million

Year 1-10: 252 million each year

\(NPV = -800 + (252/1.15) + (252/1.15)² + ... + (252/1.15)¹⁰\)

\(NPV = -800 + 204.35 + 167.55 + ... + 34.69 = 35.45\)

For Project Y:

Year 0: -850 million

Year 1-10: 250 million each year

\(NPV = -850 + (250/1.15) + (250/1.15)² + ... + (250/1.15)¹⁰\)

\(NPV = -850 + 216.09 + 176.85 + ... + 36.68 = -67.98\)

For Project Z:

Year 0: -930 million

Year 1-10: 290 million each year

\(NPV = -930 + (290/1.15) + (290/1.15)² + ... + (290/1.15)¹⁰\)

\(NPV = -930 + 235.45 + 192.62 + ... + 39.87 = -73.49\)

Based on the calculations, the most appropriate investment for Delta Corporation is Project X, as it has the highest NPV of $35.45 million. Therefore, Delta Corporation should proceed with Project X.

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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