Find the value of w and YZ if Y is between X and Z.
XY = 4w YZ = 6W XZ = 12w - 8​

The surface area of the prism formed by the net is 538 square feet².

The area occupied by the surfaces of an object is called its surface area. In geometry, different 3D shapes have different surface areas which can be easily calculated using the formula:

\(\boxed{\bold{\sf SA= 2 \times(lw + wh + lh)}}\)

Let,

So,

\(\sf SA= 2\times(45+80+144)\)

\(\sf SA =2\times269\)

\(\sf SA =\bold{538 \ square \ feet^2}\)

Thus, the surface area of the prism formed by the net is 538 square feet².

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Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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The given differential equations involve Bessel functions as solutions. The first equation requires solving for Bessel functions of the first kind, while the remaining equations involve modified Bessel functions.

1. For the differential equation 1x²y" + xy² + (x²·)y = 0, the solution can be expressed in terms of Bessel functions of the first kind (J_n(x)). The general solution is given by y(x) = c_1*x^(1/2)*J_(1/2)(2/3*x^(3/2)) + c_2*x^(1/2)*Y_(1/2)(2/3*x^(3/2)), where c_1 and c_2 are constants and Y_n(x) is the Bessel function of the second kind.

2. The second differential equation, 16x²y" + xy² + +(9x²²-)y = 0, can be transformed by substituting z = 3x^2. The equation becomes z²y" + zy² + (z²-9/4)y = 0. The solution involves modified Bessel functions of the second kind (K_n(x)). The general solution is given by y(x) = c_1*x^(1/2)*I_(1/2)(2/3*x^(3/2)) + c_2*x^(1/2)*K_(1/2)(2/3*x^(3/2)), where I_n(x) is the modified Bessel function of the first kind.

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The equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

In the given equation we have to find the equation of circle with center and radius.

The given center is (-3, -5).

Radius = 4

The standard equation of a circle with center and radius.

(x−a)^2+(y−b)^2=r^2

where a and b represent a point of center and r represent a radius.

So a=-3, b=-5 and r=4.

Putting the value in the standard equation.

(x−(-3))^2+(y−(-5))^2=(4)^2

Simplifying

(x+3)^2+(y+5)^2=16

Hence, the equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

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Option C: 0.8889 is the probability of choosing an orange marble and a green marble.

So there are in total 10 marbles.

Two marbles can be chosen in \(^{10}C_2\) ways = 90/8

Now the favorable event is when one green marble and one orange marble  is chosen. The number of ways this can be done is \(^{2}C_1 \times ^{2}C_1 = 4\)

The resultant probability is calculated by:

\(P(E) = \dfrac{Number \:of\: Favourable \:cases}{ Number\: of\: total \:cases}\\= \dfrac{4}{\frac{90}{2}}\\\\= \dfrac{8}{90}\\\\\approx 0.08889\)

Thus the needed probability is 0.08889 given by option C.

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Answer:

x = 52

Step-by-step explanation:

180 - 72 = 108

108 + 20 + x = 180

128 + x = 180

180 - 128 = x

x = 52

Have a nice day!

Answer:

Brainliest Answer?

( 7 / 8 ) seconds

( 77 / 4 ) feet

Step-by-step explanation:

The question is a bit confusing but I will do it both ways. I will assume that you made a mistake copying over the function because the graph s( t ) is linear. Linear functions have a maximum value of infinity because it is an odd-degree polynomial.

Assume that s( t ) = - 16t² + 28t + 7;

The equation forms an upside-down parabola which means it has a maximum value.

Complete the square to get the axis of symmetry and the maximum value of the parabola or use my very cool formula. The variables h and k represent the axis and max respectively.

ax² + bx + c = a( x - h )² + k;

ax² + bx + c = a( x - ( - b / 2a ) )² + c - ( b² / 4a );

ax² + bx + c;

Take a as a factor.

a( x² + ( b / a )x + ( c / a ) );

Add and subtract the square of ( 1 / 2 ) of ( b / a ). This is called completing the square because it forms a perfect square trinomial.

a( x² + ( b / a )x + ( b / 2a )²  - ( b / 2a )² + ( c / a ) );

Factorise the trinomial.

a( ( x + ( b / 2a ) )² - ( b / 2a )² + ( c / a ) );

Use the distributive property of multiplication.

a( x + ( b / 2a )² + a( ( c / a ) - ( b / 2a )² );

a( x + ( b / 2a )² +  a( ( c / a ) - ( b² / 4a² ) );

Simplify the fractions.

a( x + ( b / 2a )² + c - ( b² / 4a );

Substitute the values.

- 16( t - ( - 28 / 2( - 16 ) )² + 7 - ( ( 28 )² / 4( - 16 ) );

Time is the x-axis so we need to solve for the axis of symmetry.

h = ( - 28 / 2( - 16 ) );

h = ( - 28 / - 32 );

Simplify the fraction.

h = ( 7 / 8 );

Maximum height is the parabola's y of the vertex.

k = 7 - ( ( 28 )² / 4( - 16 ) );

k = 7 - ( ( 28 )( 28 ) / - 64 );

k = 7 - ( 784 / - 64 );

k = 7 - ( - 49 / 4 );

k = ( 28 / 4 ) + ( 49 / 4 );

k =  77 / 4;

The solution to this equation is x = 1, as 2log3x = 1 implies that log3x = 1/2, and then log3(x2 - 2) = 1/2.

The equation log3x log3(x2 2) = 1 2log3x can be simplified to log3x2 - log32 = 1 2log3x. This equation can be further simplified by combining like terms on both sides, resulting in log3x2 - 2log3x = log32. We can now take the logarithm of both sides, resulting in x2 - 2x = 2. This equation can be rearranged to x2 - 2x - 2 = 0, and then solved using the quadratic formula. The solutions of this equation are x = 1 and x = 2. However, since log3x must be positive, the only valid solution to the equation is x = 1. This implies that 2log3x = 1, and then log3(x2 - 2) = 1/2. Therefore, the solution to the equation log3x log3(x2 2) = 1 2log3x is x = 1.

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Answer:

P = 2w - 10

Step-by-step explanation:

To solve this problem use the perimeter formula \(P=2l+2w\)

So here we have 1 as the width and w-6 as the length \(P=2(w-6) + 2(1)\)

So we multiply 2(w) 2(-6) to get 2w-12

So because 2 times 1 is 2 the perimeter would be \(P=2w-12 + 2\)

Simplified would be \(P=2w-10\)

because -12 + 2 = 10

Hopes this helps

Answer: Where is the figure??

Answer:

I think it this one but picture would help...

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.  

Answer: 7

Step-by-step explanation:

The main difference between an area variance and a use variance is that area variance allows for an exception to zoning regulations related to the physical characteristics of a property, while use variance allows for an exception to regulations related to the intended use of a property.

An area variance is typically granted when a property owner is unable to comply with zoning regulations related to setbacks, building height, lot coverage, or other physical characteristics of a property.

In contrast, a use variance allows a property owner to use their property for a purpose that is not permitted under the current zoning regulations. This may include using a residential property for commercial purposes or using a commercial property for residential purposes.

Use variances are generally more difficult to obtain than area variances, as they require a showing of a unique hardship or practical difficulty that cannot be addressed through other means.

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The length of line segment K′N′ from the trapezoid KLMN cannot be determined based on the given information. More information is needed to answer this question accurately.

The length of line segment K′N′ will be the same as the length of line segment KN in the original trapezoid KLMN. This is because a reflection across the x- or y-axis does not change the length of any line segments, it only changes their position.

To find the length of line segment KN, we can use the distance formula:

KN = √((x2 - x1)² + (y2 - y1)²)

Where x1 and y1 are the coordinates of point K, and x2 and y2 are the coordinates of point N.

Without knowing the coordinates of points K and N, it is not possible to determine the length of line segment KN or K′N′. Therefore, more information is needed to answer this question accurately.

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Using the combination formula, it is found that there are 16,800 ways for them to do it.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, we have that:

Hence the number of ways is:

\(N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800\)

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The parameterized plane that contains the three points is r(s,t) = (1,−2,−5) + s(−11,−4,−7) + t(14,22,15).

To parameterize the plane that contains the three points (1,−2,−5), (−10,−6,−12), and (15,20,10), we can use a vector equation.

We can choose any of the given points as r. Let's choose (1,−2,−5) as our r

r = (1,−2,−5).

To find v, we need to subtract r from any two points on the plane. Let's choose (−10,−6,−12) and (15,20,10) as our points.

⃗v = (−10,−6,−12) - (1,−2,−5) = (−11,−4,−7).

Similarly, we can subtract r from another pair of points. Let's choose (−10,−6,−12) and (15,20,10) again.

⃗w = (15,20,10) - (1,−2,−5) = (14,22,15).

Now we have all the necessary components to parameterize the plane.

r(s,t) = (1,−2,−5) + s(−11,−4,−7) + t(14,22,15).

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The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.

In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.

Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.

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The vehicle travels 110 feet distance in 1 second duration.

mph expresses the speed or velocity in miles per hour. Speed means rate of change of distance with respect to time.

speed = distance/time

hence, distance = speed x time

the above equation is the relationship between distance, speed and time

we will use the above equation and convert miles to feet and second to hour.

given, speed of vehicle = 75 mph

time = 1 second =1/3600 hour as 1 hour = 3600 second

distance travel by vehicle = speed x time

                                            = 75 mph x 1/3600 hour

                              distance              = 0.020833333 miles

               we know, 1 mile =5280 feet

  distance in feet = 110 feet

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Herefore, the plane was flying at a height of approximately 31680.30 feet or 6.00 miles when it passed over the George Washington Bridge.

a. To determine the height of the plane when it passed over the George Washington Bridge, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the height of the plane is the hypotenuse, and the distance from the bridge to the landing location is one of the other sides.

First, we need to convert the distance from miles to feet, as the height of the bridge is given in feet:

6 miles = 6 * 5280 feet = 31680 feet

Using the Pythagorean theorem, we have:

Height of plane = sqrt(212^2 + 31680^2) feet

Height of plane = 31680.30 feet (rounded to two decimal places)

To convert this height to miles, we divide by the number of feet in a mile:

Height of plane = 31680.30 / 5280 miles

Height of plane = 6.00 miles (rounded to two decimal places)

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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Answer:

18,000 forks

Step-by-step explanation:

They are making 3,000 forks each hour for 6 hours, so you would multiply 3,000 by 6. 3,000 multiplied by 6 is 18,000.

Answer:

The factory will make 18,000 plastic forks in 6 hours

Step-by-step explanation:

Hope this helps :)

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Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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Answer:

11

Step-by-step explanation:

5%=0.05

0.05x220=11

Answer:

Im guessing 11.

Step-by-step explanation:

5% of 220 is 11.

Solution

Given that

sample size n = 11

The degree of freedom df = n - 1 = 11 - 1 = 10

At 99% confidence level,

Checking the table,

Therefore, the Critical value t value = 3.169

Answer:

1/2

Step-by-step explanation:

Answer:

154 minutes

Step-by-step explanation:

It takes him 2.8 minutes per page (462 / 165)

2.8 times 55 is 154

Answer:

It would take Raymond 154 mins to read 55 pages

Step-by-step explanation:

Use simple proportion

165 pages in 462 mins

55 pages in Xmins

Cross multiply

55×462= 165× X

X= 55×462/165

X= 154 mins

The equation to model the situation is \(\mathbf{y = \dfrac{k}{x^2}}\). The constant for the variation is 2250.

The intensity of light from a lantern varies inversely to the square of the distance from the lantern.

From the given information:

Then:

\(\mathbf{y \alpha \dfrac{1}{x^2} }\)

\(\mathbf{y = \dfrac{k}{x^2} }\)   here, k = constant.

2.

If y = 90 W/m² when the distance x = 5m

Then:

\(\mathbf{90 = \dfrac{k}{(5)^2}}\)

k = 90 × 25

k = 2250

c.

The equation to model the situation by using the constant variation is:

\(\mathbf{y = \dfrac{2250}{x^2}}\)

d.

If the light intensity y = 40, then x is determined as:

\(\mathbf{40 = \dfrac{2250}{x^2}}\)

\(\mathbf{x = \sqrt{\dfrac{2250}{40}}}\)

x = 7.5 m

e.

The light is needed in (225 × 1000)m = 225000 km of illumination.

f.

The lantern required for the new light estimation is:

y = 2250/225000

y = 0.01 intensity

Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.

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The Stokes approximation and Oseen approximation are methods used to determine the motion of fluid particles in a fluid dynamics problem.

The Stokes approximation applies to slow-moving fluid particles, where viscous forces are dominant, while the Oseen approximation applies to higher velocities, where convective forces are dominant..Oseen approximation: In this approximation, the equations governing the motion of fluid particles account for the convective forces in addition to the viscous forces.

This approximation is valid at moderate Reynolds numbers and is used when the viscous forces are still strong but not as dominant as in the Stokes approximation. The velocity of the fluid decreases less rapidly than in the Stokes approximation, and the approximation is valid for Reynolds numbers greater than one .The difference between the results of the two approximations lies in their range of applicability and the accuracy of their results.

The significance of the difference between the two approximations lies in their application to real-world problems. In fluid dynamics, it is essential to have accurate approximations to predict the behavior of fluid particles accurately. Therefore, choosing the appropriate approximation for the specific problem is critical. knowing the range of applicability of each approximation can help in determining the parameters for the problem.

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Answer:

Paul is wrong.

Step-by-step explanation:

He did not add the exponents right in this equation. The right answer would be 5.67 * 10^9.

I hope this helped. : )