Which are equivalent?

Answer:

y = ½x + 2

Step-by-step explanation:

We are given the coordinates of the endpoint as;A(8,2) and

B(0,6)

The midpoint coordinates will be;

((8 + 0)/2, (2 + 6)/2) = (4, 4)

The slope of the midpoint using gradient formula will be;

m = (6 - 2)/(0 - 8)

m = 4/-8

m = -2

Thus, slope of a line perpendicular to the midpoint is;

m_p = -1/m

m_p = -1/-2

m_p = 1/2

Thus, using slope intercept concept, the equation to represent the perpendicular bisector is;

y - 4 = ½(x - 4)

Multiply both sides by 2 to get;

2y - 8 = x - 4

Add 8 to both sides to get;

2y - 8 + 8 = x - 4 + 8

2y = x + 4

Divide through by 2 to get;

y = ½(x + 4)

y = ½x + 2

The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.

The solution of the system of equations using Cramer's rule is calculated as follows;

The given equations are as follows;

9x - 2y = -9

-3x - 8y = 1

The determinant of the coefficient matrix is calculated as;

D = [9      -2]

      [-3     -8]

D = -8(9) - (-3 x - 2)

D = -72 - 6 = -78

The x coefficient is calculated as;

Dx = [-2      -9]

       [ -8       1]

Dx = -2(1) - (-8 x -9)

Dx = -2 - 72 = -74

The y coefficient is calculated as;

Dy = [9      -9]

       [ -3       1]

Dy = 9(1) - (-3 x -9)

Dy = 9 - 27 = -18

The x and y values is calculated as;

x = Dx/D  = -74/-78 = 74/78 = 37/39

y = Dy/D = -18/-78 = 18/78 = 9/39

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Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

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Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

The probability that at most 24 heads occur 0.00000077.

We can model the number of heads as a binomial random variable with n = 25 and p = 0.5.

We want to find the probability that at most 24 heads occur, which is the same as finding the probability that 0, 1, 2, ..., or 24 heads occur.

Using a binomial probability table or calculator, we can find the individual probabilities for each outcome and then add them up:

P(X ≤ 24) = P(X = 0) + P(X = 1) + ... + P(X = 24)

= 0.00000003 + 0.00000075 + 0.00001216 + 0.00013733 + 0.00109392 + 0.00663471 + 0.03192139 + 0.11641502 + 0.30035400 + 0.50000000

= 0.95566955

Therefore, the answer is (e) 0.99999923 (rounded to 8 decimal places).

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Answer:

Step-by-step explanation:

12x-34

Add all the sides together

2(x+3) + 6x + 4(x – 10)

distribute:

2x+6 + 6x + 4x-40

and add:

12x-34

The graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points.

The answer is (C) Three.To determine the number of points where the graph of the equation y = x(x² - 2)(x² + x + 1) intersects the x-axis, we need to find the x-values that make the equation equal to zero.

Setting y = 0, we have:

0 = x(x² - 2)(x² + x + 1)

Since the product of three factors is zero, at least one of the factors must be zero.

1. Setting x = 0:

0 = 0(x² - 2)(x² + x + 1)

This gives us one solution: x = 0.

2. Setting x² - 2 = 0:

x² = 2

Taking the square root of both sides:

x = ±√2

This gives us two additional solutions: x = √2 and x = -√2.

3. Setting x² + x + 1 = 0:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, there are no real solutions for this quadratic equation.

In summary, we have found three different x-values where the equation intersects the x-axis: x = 0, x = √2, and x = -√2.

Therefore, the graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points. The answer is (C) Three.

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The width of the sidewalk is approximately 3.21 feet (rounded to two decimal places).

Let's use the given information to solve for the width (x) of the sidewalk. The area of the rectangular swimming pool is 20 feet by 30 feet, which equals 600 square feet (20*30 = 600).

The total area of the pool and sidewalk is given as 825 square feet. To find the area of just the sidewalk, we subtract the area of the pool from the total area: 825 - 600 = 225 square feet.

Now, let's express the area of the sidewalk using the dimensions of the pool and the width of the sidewalk (x). Since the sidewalk is on 3 sides, we can represent the area as follows:

2(20x) + 30x = 225

Simplify the equation:

40x + 30x = 225

Combine the terms:

70x = 225

Now, solve for x:

x = 225 / 70

x ≈ 3.21

The width of the sidewalk is approximately 3.21 feet (rounded to two decimal places).

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The angle of elevation from Row A to the bottom of the screen 13.3.

The angle of depression from Row P to the bottom of the screen 4.4

let angle of elevation of Row A to the bottom of the Screen be Ae

So, tan Ae = 2.5 - 5.8tan 11  /5.8

tan Ae = 0.23665

Ae = 13.3

Now, let the angle of depression of Row P to the bottom of the screen be P

tan P  =  2.3 tan 11- 2.5/ 2.5

tan P = 0.077

P = 4.4

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To find out how many eggs Clarence used for a batch of each dessert, we can set up a system of equations based on the information provided.

Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies based on the information and the solution to the system of equations.

Let's represent the number of eggs used for a batch of brownies as 'b' and the number of eggs used for a batch of cookies as 'c'.

From the given information:

In the previous month, 2 batches of brownies and 2 batches of cookies required a total of 6 eggs:

2b + 2c = 6 -- Equation 1

In the month before, 2 batches of brownies and 1 batch of cookies required a total of 4 eggs:

2b + c = 4 -- Equation 2

We can now solve this system of equations to determine the number of eggs used for a batch of each dessert.

Multiplying Equation 2 by 2, we have:

4b + 2c = 8 -- Equation 3

Subtracting Equation 3 from Equation 1, we can eliminate 'b':

(2b + 2c) - (4b + 2c) = 6 - 8

-2b = -2

b = 1

Now that we have found the value of 'b' to be 1, we can substitute it back into Equation 2 to solve for 'c':

2(1) + c = 4

2 + c = 4

c = 2

Therefore, Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies.

In conclusion, Clarence used 1 egg for a batch of brownies and 2 eggs for a batch of cookies based on the given information and the solution to the system of equations.

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TCP provides error checking to ensure reliable data delivery, making option A the correct answer. Only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

TCP (Transmission Control Protocol) provides error checking as part of its services. It ensures reliable data delivery by using acknowledgments and sequence numbers to detect and recover from packet loss, errors, or out-of-order delivery. When a TCP receiver receives data, it sends an acknowledgment (ACK) back to the sender to confirm the successful reception of packets. If the sender does not receive an ACK for a particular packet within a specified timeout period, it assumes the packet was lost or damaged and retransmits it.

TCP provides error checking to ensure reliable data delivery, making option A the correct answer.

The propagation delay is the time it takes for a signal to travel from the source to the destination. It is determined by the physical distance between the devices and the speed of signal propagation in the transmission medium. The propagation delay is an inherent characteristic of the medium and cannot be eliminated by switching devices or other strategies.

The other three options—processing delay, queuing delay, and transmission delay—are all caused by the store-and-forward strategy used by switching devices. Processing delay refers to the time taken to examine and process the packet headers. Queuing delay occurs when packets have to wait in a queue before being transmitted. Transmission delay is the time it takes to push the bits onto the transmission medium.

Among the given options, only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

3. The correct answer is A. The system is very well-engineered.

In a statistical multiplexing system, the queuing delay is the delay experienced by packets waiting in a queue before being transmitted. If the average queuing delay is very close to zero, it indicates that the system is well-engineered and efficiently managing its resources. A well-designed system can minimize or eliminate queuing delays by appropriately allocating resources and ensuring efficient scheduling algorithms.

Traffic intensity, which represents the ratio of the average traffic load to the transmission capacity, does not directly determine the queuing delay. It is possible to have low queuing delays even with high traffic intensity if the system is well-designed.

When the average queuing delay is close to zero, it suggests that the system is well-engineered and efficiently utilizing its resources, as stated in option A.

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Answer:

267.94

Step-by-step explanation:

V=4/3(pi)r^2

V=4/3(3.14)8^2

V=4/3(3.14)64

V=4/3(200.96)

V=267.94

Answer:

2144.7 m^3

Step-by-step explanation:

The dive of the Peregrine falcon took 7.5 seconds

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

Assuming the top speed of  a Peregrine falcon is 240mph.

Distance travelled by the Peregrine falcon = 0.5 miles

By using the formula we get

0.5 = 240 x time

time = \(\frac{1}{480}\) hours

time = \(\frac{3600}{480}\) seconds = 7.5 seconds

∴ The dive of the Peregrine falcon took 7.5 seconds

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The 80% confidence interval for the population mean is given as follows:

(4.34, 5.66).

The sample mean, the population standard deviation and the sample size are given as follows:

\(\overline{x} = 5, \sigma = 2, n = 15\)

The critical value of the z-distribution for an 80% confidence interval is given as follows:

z = 1.28.

The lower bound of the interval is given as follows:

\(5 - 1.28 \times \frac{2}{\sqrt{15}} = 4.34\)

The upper bound of the interval is given as follows:

\(5 + 1.28 \times \frac{2}{\sqrt{15}} = 5.66\)

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Answer:

is it like exponets

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

12*2=24

7*3=24

3*7=24

4*6=24

Hope this helps!

Answer:

7

Step-by-step explanation:

note that 7³ = 343

then

\(\sqrt[3]{343}\)

= \(\sqrt[3]{7^3}\)

= 7

The slope of the line is represented by the word m which is obtained as 0.5.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

To determine a line's inclination or steepness, use the slope formula. Calculating the ratio of the change in the y-axis to the change in the x-axis may be used to calculate the slope of any line.

From the graph, the data is observed as,

(x₁,y₁)=(0,1)

(x₂,y₂) = (-2,0)

The slope of the line is found as,

\(\rm m =\dfrac{0-1}{-2-0} \\\\ m = 0.5\)

Thus, the slope of the line is represented by the word m which is obtained as 0.5.

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Answer:

90° is the smallest amount you need to rotate the image for it to look the same.

The smallest no. of degrees we need to rotate this image to look the same is 45°.

Rotational symmetry is a property of a given figure is when it is rotated about some degrees it looks the same as before we can rotate it by 0°≤Ф<360°.

According to the given question

The image has rotational symmetry.

We can think of this image as a circle

∴ A complete circle has 360°

The figure has 8 wings.

So, the smallest no. degrees that can be rotated that makes this figure satisfying rotational symmetry is

360/8

=45°

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A pair (x, p) is an equilibrium, if and only if x and p are optimal solutions to the standard form problem and its dual, respectively.

To show that a pair (x, p) is an equilibrium if and only if x and p are optimal solutions to the standard form problem and its dual, we need to demonstrate both directions of the equivalence.
First, let's assume that (x, p) is an equilibrium. An equilibrium occurs when the primal problem and its dual problem satisfy certain conditions. In this case, we have:
1. Primal problem:
  - Objective function: maximize \(c^T * x\) (where c is the cost vector and x is the decision variable)
  - Subject to: Ax = b (where A is the constraint matrix and b is the right-hand side vector)
2. Dual problem:
  - Objective function: minimize \(b^T * p\) (where p is the dual variable)
  - Subject to: \(A^T * p \geq c\) (where \(A^T\) is the transpose of A)
Now, if (x, p) is an equilibrium, it means that both the primal and dual problems are feasible, and their objective functions are equal. This implies that x and p are optimal solutions to their respective problems.
Conversely, let's assume that x and p are optimal solutions to the standard form problem and its dual, respectively. This means that x and p satisfy the feasibility conditions and optimize the objective functions of their respective problems.
Since x and p are optimal solutions, the objective functions of the primal and dual problems are equal. This condition ensures that (x, p) is an equilibrium.

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A pair (x, p) is an equilibrium if and only if x is an optimal solution to the standard form problem and p is an optimal solution to its dual. Both conditions must be satisfied for equilibrium.

To show that a pair (x, p) is an equilibrium, we need to prove two conditions: (1) x is an optimal solution to the standard form problem, and (2) p is an optimal solution to its dual.

First, assume that (x, p) is an equilibrium. This means that x is feasible and satisfies the constraints of the standard form problem. We can also assume that p is feasible and satisfies the constraints of the dual problem.

To prove condition (1), we can use contradiction. Suppose x is not an optimal solution. Then there exists another feasible solution x' that yields a better objective function value. However, this contradicts the definition of an equilibrium, so x must be an optimal solution.

Similarly, to prove condition (2), we can assume that p is not an optimal solution. Then there exists another feasible solution p' to the dual problem that yields a better objective function value. Again, this contradicts the definition of an equilibrium, so p must be an optimal solution.

Conversely, if x is an optimal solution to the standard form problem and p is an optimal solution to its dual, we can conclude that (x, p) is an equilibrium. This is because both x and p satisfy the necessary conditions for optimality.

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Answer:

13cm

Step-by-step explanation:

if the area is 117 then to find out the missing length, you divide 117 by 9 which gets you 13.

to check its correct, 13 x 9 = 117cm^2

If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

Answer:

90

Step-by-step explanation:

9^2 = 81 and 3^2 = 9

81 + 9 = 90

Answer:

90

Step-by-step explanation:

9² + 3²

= (9 x 9) + (3 x 3)

= 81 + 9

= 90

Answer:

A circle is the set of all points in a plane equidistant from a given point.

Step-by-step explanation:

A circle is a shape composed of a single line or set of points that have the same distance from the center of the circle or that are equidistant from the center.

Answer: a circle have no sides or no cornors

Step-by-step explanation:

Answer:

-3, 2

Step-by-step explanation:

Please give me brainlist

Answer:

y = 2x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 2)

m = \(\frac{2+2}{2-0}\) = \(\frac{4}{2}\) = 2

The line crosses the y- axis at (0, - 2) ⇒ c = - 2

y = 2x - 2 ← equation of line

The volume of the igloo is 523.43 m^3

We know that the volume of a sphere of radius R is:

\(V = (4/3)*pi*R^3\)

Where pi = 3.14

Then the volume of a hemisphere is half of that.

In this case, we have a hemisphere with a radius of 6.3m, then the volume will be:

\(V = (1/2)*(4/3)*3.14*(6.3m)^3 = 523.43 m^3\)

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a).  2^38 bytes of memory

b). 12 bits

c). The maximum number of entries in the single-level page table would be 2^38.

d). The size would be 2^38 * 4KB, which equals 2^20 pages.

e). The maximum number of entries it can have depends on the remaining bits of the logical address.

f). The amount of bits required to denote an index into the inner page table is obtained by subtracting the offset and outer page index bits from the logical address.

a. To address a physical memory size of 128GB (2^37 bytes), a 64-bit architecture would require 38 bits for the logical address, allowing access to a maximum of 2^38 bytes of memory.

b. Given that the page size is 4KB (2^12 bytes), 12 bits would be needed to specify the displacement into a page. This means that the lower 12 bits of the logical address would be used for page offset or displacement.

c. With a single-level page table, the maximum number of entries would be equal to the number of possible logical addresses. In this case, since the logical address requires 38 bits, the maximum number of entries in the single-level page table would be 2^38.

d. The size of the single-level page table is determined by the number of entries it contains. Since each entry maps to a page of size 4KB, the size of the single-level page table can be calculated by multiplying the number of entries by the size of each entry. In this case, the size would be 2^38 * 4KB, which equals 2^20 pages.

e. For a two-level page table, the size of the outer page table is determined by the number of entries it can contain. Since the outer page table uses 4KB pages, the maximum number of entries it can have depends on the remaining bits of the logical address. The number of bits used for the index into the outer page table is determined by subtracting the bits used for the inner page index and the offset from the total number of bits in the logical address.

f. The number of bits used to specify an index into the inner page table can be determined by subtracting the bits used for the offset and the bits used for the outer page index from the total number of bits in the logical address. The remaining bits are then used to specify the index into the inner page table.

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