whats the area of this figure​

The distance between the given pair of parallel lines is 21 units.

The pair of parallel lines given by the equations x = 8.5 and x = -12.5 are vertical lines. The distance between them is the distance between their x-coordinates.

Coplanar infinite straight lines that are parallel have no points of intersection. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

This can be found by subtracting the smaller x-coordinate from the larger one as follows:

Distance between the given pair of parallel lines = Larger x-coordinate - Smaller x-coordinate= 8.5 - (-12.5)= 8.5 + 12.5= 21 units

Therefore, the distance between the given pair of parallel lines is 21 units.

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The volume of the given solid enclosed by the paraboloids y = x2 + z2andy = 72 − x2 − z2 is 10368 cubic units.

Using a triple integral, we will integrate over the region of the xz-plane that is enclosed by the paraboloids.

The limits of integration for x and z can be found by solving the two equations for x^2 + z^2:

$x^2 + z^2 = y = x^2 + z^2 + 72 - x^2 - z^2$

$x^2 + z^2 = 36$

Therefore, the limits of integration for x and z are from -6 to 6.

The limits of integration for y are from the equation of the lower paraboloid $y = x^2 + z^2$ to the equation of the upper paraboloid $y = 72 - x^2 - z^2$.

Therefore, the limits of integration for y are from $x^2 + z^2$ to $72 - x^2 - z^2$.

The triple integral for the volume of the solid is:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} \int_{x^2+z^2}^{72-x^2-z^2} dy dz dx$

Integrating with respect to y:

$\int_{x^2+z^2}^{72-x^2-z^2} dy = 72 - 2(x^2 + z^2)$

Substituting this into the triple integral gives:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} (72 - 2(x^2 + z^2)) dz dx$

Integrate with respect to z:

$\int_{-6}^{6} (72 - 2(x^2 + z^2)) dz = 72(12) - 4x^2(6) = 864 - 24x^2$

Integrate with respect to x:

$\int_{-6}^{6} (864 - 24x^2) dx = 2(864)(6) - 2\int_{0}^{6} (24x^2) dx = 10368$

Therefore, the volume of the solid enclosed by the paraboloids $y = x^2 + z^2$ and $y = 72 - x^2 - z^2$ is 10368 cubic units.

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Answer:

A crumpled paper ball has a reduced area as compared to a sheet of paper which has a larger surface area. So, the sheet of paper will face a lot of air resistance when the sheet of paper is dropped from a height as its area is large. Thus, the speed of the sheet decreases and it will fall at a slower rate.

Step-by-step explanation:

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

For the expressions 4x+5+x+9 and 9x+10 to be equivalent, they must have the same value for any value of x.

So we can set the two expressions equal to each other and solve for x.

4x + 5 + x + 9 = 9x + 10

Simplifying the left side:

5x + 14 = 9x + 10

Subtracting 5x from both sides:

14 = 4x + 10

Subtracting 10 from both sides:

4 = 4x

Dividing both sides by 4:

x = 1

So the expressions 4x+5+x+9 and 9x+10 are equivalent when x = 1.

The unit tangent vector t(t) is (3, 4t, 2t) / sqrt(9 + 20t^2), and the unit normal vector n(t) is (3, 4, 2t) / sqrt(25 + 4t^2).

The unit tangent vector t(t) of the given vector function r(t) = (3t, 1 + 2t^2, t^2) is obtained by dividing the derivative of r(t) by its magnitude. The derivative of r(t) is (3, 4t, 2t), and the magnitude of this vector is sqrt(9 + 20t^2). Therefore, t(t) = (3, 4t, 2t) / sqrt(9 + 20t^2).

The unit normal vector n(t) can be obtained by dividing the derivative of t(t) by its magnitude. The derivative of t(t) is (3, 4, 2t), and the magnitude of this vector is sqrt(25 + 4t^2). Thus, n(t) = (3, 4, 2t) / sqrt(25 + 4t^2).

These unit vectors t(t) and n(t) represent the direction of motion and the direction of the curve's curvature at each point t, respectively, providing valuable information about the behavior of the vector function r(t).

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The new length of the unstretched hanging-spring is 70 cm.

Hooke's law states that the spring's length change as a result of a compressive or tensile load is directly proportionate to the size of the force placed on the spring. Mathematically,

F = kx

Where;

K is the spring constant, while x represents the spring's length change.

As per the question-

L is the spring's uncompressed length: L = 0.5 m

Weight F1 linked to the spring: F1 = 100 N

First weight's effect on elongation x1: 60 - 50 = 10 = .01 m.

As per the Hooke's law;

F1 = Kx1

K = F1/X1

K = 100 / 0.1

K = 1000 N/m

Spring constant = 1000 N/m.

For the added 100-N block.

F = Kx2

x2 = F/K

x2 = 100 + 100 / 1000

x2 = 0.2m

x2 = 20 cm

L = 50 + 20 = 70 cm.

Thus, new length of the unstretched hanging-spring is 70 cm.

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Answer:

Factors

Step-by-step explanation:

To find the roots of a polynomial, [factors] help the process of finding them

Answer:

No, it does not.

Step-by-step explanation:

This does not make a right triangle because in order to have a right triangle you must have 2 of the same numbers.

For example:

900, 800, 900 makes a right triangle

900, 800, 700 does not.

Hope this helped :D

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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The value of the expression at, a= 4, c = 2, and d = - 2.5 is 18768.75.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression -11с(а - d) + 121c²(a - d)² at, a= 4, c = 2 and d = - 2.5.

Simplifying the expression -11с(а - d) + 121c²(a - d)² we have,

= -11с(а - d) + (11c)²(a - d)².

= - 11c[(a - d) - 11c(a - d)²].

= - 11×2[4 + 2.5) - 11×2(4 + 2.5)²].

= - 22[6.25 - 22(6.25)²].

=  - 22[6.25 - 22×39.0625].

= - 22[6.25 - 859.375].

= - 22[- 853.125].

= 18768.75.

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Answer:

22 hours = hours travelling altogether

Step-by-step explanation:

11 x 2 = 22

Answer:

C.

Step-by-step explanation:

Answer: A) x axis

Step-by-step explanation:

goes through the origin

Answer:

1800.

Step-by-step explanation:

Multiply them all.

\(12 * 15* 10 = 1800.\)

The answer is 1800.

Area: 1800 feet cubed

Surface Area: 900 feet square

When the sample size is increased, the LCL comes closer to the process mean and the UCL moves farther from the process mean.Hence, (c) When a Type I error is made, the process will be declared out of control and adjusted when the process is actually in control.

(d) When a Type II error is made, the process will be declared in control and allowed to continue when the process is actually out of control. The probability of a Type I error for a sample of size 10 is 0.0027, for a sample of size 20 is 0.0014, and for a sample of size 30 is 0.0010. Increasing the sample size provides a more accurate estimate of the process mean and reduces the probability of making a Type I error.

The advantage of increasing the sample size for control chart purposes is that the error probability is reduced as the

When the sample size is increased, the LCL comes closer to the process mean and the UCL moves farther from the process mean.The process will be declared out of control and adjusted when the process is actually in control.When a Type II error is made, the process will be declared in control and allowed to continue when the process is actually out of control.

The probability of a Type I error for a sample of size 10 is 0.0027, for a sample of size 20 is 0.0014, and for a sample of size 30 is 0.0010.The advantage of increasing the sample size for control chart purposes is that the error probability is reduced as the sample size is increased.

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Perks A Lot has both a higher median and a higher mean value, indicating that it typically sells more coffee per hour than Wide Awake. Perks A Lot, with a median value of 5.75 gallons i.e. A.

What exactly is a median?

In statistics, the median is a measure of central tendency that represents the middle value of a data set. To find the median, the data set must first be arranged in order from smallest to largest (or largest to smallest).

If the data set has an odd number of values, then the median is the middle value. For example, in the data set 2, 5, 7, 8, 10, the median is 7 because it is the middle value.

If the data set has an even number of values, then the median is the average of the two middle values. For example, in the data set 3, 4, 6, 9, the median is (4+6)/2 = 5.

Now,

To compare the data and determine which shop typically sells the most amount of coffee per hour, we need to calculate the measures of central tendency for each set of data.

For Perks A Lot:

Median: To find the median, we need to order the data and find the middle value. Ordering the data gives us:

2.5, 3, 3.5, 4.5, 5.5, 6, 7, 8, 9, 9.5, 10

The middle value is 5.75, so the median for Perks A Lot is 5.75 gallons.

Mean: To find the mean, we need to sum up all the values and divide by the number of values. Summing up the values gives us 63.5, and dividing by 11 (the number of values) gives us a mean of approximately 5.77 gallons.

For Wide Awake:

Median: Ordering the data gives us:

2.5, 3, 4, 4, 5, 6, 6.5, 10, 15

The middle value is 4.5, so the median for Wide Awake is 4.5 gallons.

Mean: Summing up the values gives us 49, and dividing by 9 gives us a mean of approximately 5.44 gallons.

Based on these calculations, we can see that Perks A Lot has both a higher median and a higher mean value, indicating that it typically sells more coffee per hour than Wide Awake. Therefore, the correct answer is: Perks A Lot, with a median value of 5.75 gallons.

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Answer: An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

Answer:

y=3x+4

Step-by-step explanation:

since the line is parallel it has the same slope so we have y = 3x + b. plug in the point (2,10) to get 10 = 3*2 + b, so b=4. so the equation is y = 3x +4

Answer:

i would go with B

Step-by-step explanation:

I'm not too sure I'm so sorry but thats my closest guess

The percentage of total calories consumed that should come from fat is 20 percent to 35 percent (OPTION B)

The percentage of total calories consumed that should come from fat is 20 percent to 35 percent (option b). This recommendation is based on the Dietary Guidelines for Americans and ensures a balanced diet to maintain optimal health. Here's a step-by-step explanation:
Understand the question: You are asked to determine the recommended percentage of total calories that should be obtained from fat in a balanced diet.
Review the given options: The provided options are a) 5% to 15%, b) 20% to 35%, c) 30% to 40%, and d) 10% to 25%.
Recall the recommended guidelines: According to the Dietary Guidelines for Americans, the appropriate percentage range of total calories from fat is 20% to 35%.
Identify the correct option: Based on the guidelines, option b (20% to 35%) is the correct answer.
Provide the answer: The percentage of total calories consumed that should come from fat is 20 percent to 35 percent (option b). This recommendation ensures a balanced diet to maintain optimal health.

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Answer:

A. 90

Step-by-step explanation:

It says the scale is 1:6, so we can multiply 15 square cm to, 15 x 6 = 90 square cm!

Hope this Helps! :)

Answer:

A. 90 square cm

Step-by-step explanation:

The scale factor is 1:6

So the scale drawing on the left is the 1.

The object on the right is 6.

The area of the scale drawing is 15 square cm. If we multiply that by 6, we get answer A. 90 square cm.

Answer:

IT'S A. HEHEHEHEHEHEHE

The piece-wise function graphed is defined as follows:

The parameters are as follows:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

In this problem, the graphed function has to definitions, as follows:

To the left of x = 1, the linear function has:

Thus the definition is:

f(x) = 4x - 3, if x ≤ 1.

Thus the parameters are c = 4 and d = -3.

To the right of x = 1, the linear function has:

Thus the definition is:

f(x) = 2x - 5, if x > 1.

The parameters are a = 2 and b = -5.

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Element "e" has two isotopes, e-57 with a mass of 57.977 amu and e-58 with a mass of 58.977 amu. The percentage of e-57 is approximately 50.25%, while the percentage of e-58 is approximately 49.75%.

The percentage of each isotope can be determined using the concept of weighted averages. We know the masses of the two isotopes and the average atomic weight of the element. Let's assume x represents the percentage of e-57 and y represents the percentage of e-58.

To calculate the average atomic weight, we can set up the following equation:

(x/100) * 57.977 + (y/100) * 58.977 = 58.776

Simplifying the equation, we have:

0.57977x + 0.58977y = 58.776

Now we can solve this equation to find the values of x and y. Rearranging the equation, we get:

x + y = 100 - x

0.57977x + 0.58977(100 - x) = 58.776

Solving this equation gives us x ≈ 50.25 and y ≈ 49.75.

Therefore, the percentage of e-57 is approximately 50.25%, while the percentage of e-58 is approximately 49.75%.

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Answer:

306

Step-by-step explanation:

Answer:

0

y+1= (3x-12)y+1=3x-12

The zeros of the function f(x) = \(x^4\) + 7\(x^2\) - 144x, along with their multiplicities, are x = -8 (multiplicity 1), x = 0 (multiplicity 1), x = 9 (multiplicity 2).

To find the zeros of the function f(x) = \(x^4\) + 7\(x^2\) - 144x, we set the function equal to zero and solve for x.

\(x^4\) + 7\(x^2\) - 144x = 0

Factoring out an x from the equation, we have:

x(\(x^3\)+ 7x - 144) = 0

Setting each factor equal to zero, we find the following possible zeros:

x = 0

To find the remaining zeros, we need to solve the cubic equation \(x^3\) + 7x - 144 = 0. This equation can be solved using numerical methods or factoring techniques. By applying these methods, we find the remaining zeros:

x = -8 (multiplicity 1), x = 9 (multiplicity 2)

Therefore, the zeros of f(x) are x = -8, x = 0, and x = 9, with respective multiplicities of 1, 1, and 2.

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Answer:

Step-by-step explanation:

Complementary angles are angles that add up to 90°.

We have C and D as complementary.

Their sum is:

Substitute values and solve for x:

Answer:

x = 7

Step-by-step explanation:

Complementary angles are two angles that sum up to 90°. In this case, we are given that ∠C and ∠D are complementary. This means that the sum of ∠C and ∠D is equivalent to 90°.

⇒ ∠C + ∠D = 90°

⇒ 8x + 5x - 1 = 90°                                                          [∠C = 8x; ∠D = 5x - 1]

⇒ 13x - 1 = 90°

⇒ 13x = 90 + 1

⇒ 13x = 91

⇒ 13x/13 = 91/13

⇒ x = 91/13 = 7