If x is directly propotional to y
Given that x=8 and y=2
find x=4.

Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

Answer:

Height= 4m (nearest meter)

Step-by-step explanation:

\(\boxed{volume \: of \: cone = \frac{1}{3} \pi {r}^{2}h }\)

Diameter= 2(radius)

Given that the diameter is 12m,

radius of cone

= 12 ÷2

= 6m

Let the height of the cone be h meters.

\(151 = \frac{1}{3} \pi(6^{2} )(h)\)

\(151 = 12\pi h\)

\(h = \frac{151}{12\pi} \)

h= 4.0054 (5 s.f.)

Thus, the height of the cone is 4m. (nearest meter)

The coordinates after the dilation of 1/4 are A'(2, -5), B'(6, -3), and

C'( 3, -2) and this can be determined by using the given data.

What is dilation?

Given :

Dilation Factor -  1/4

Center  -  (5,-5)

The following steps can be used in order to determine the graph the image of the figure after a dilation with a scale factor of 1/4  centered at  (5, -5):

Step 1 - According to the given graph, the coordinates of the triangle are A(-3,7), B(-7,-5), and C(9,3).

Step 2 - According to the given data, the dilation factor is 1/4.

Step 3 - The distance of the center from point A is 12 units.

= 1/4 x 12 = 3

So, A'(2,-5).

Step 4 - The distance of the center from point B is 8 units.

= 1/4 x 8 = 2

So, B'(6,-3).

Step 5 - The distance of the center from point C is 12/8 units.

= 1/4 x 12/8

= 3/2

So, C'( 3,-2).

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Image:

Image of graph is given below.

The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.

The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.

The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.

The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.

The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.

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Using sampling concepts, it is found that the sample is given by:

C. The 150 businesses who were sent surveys.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, a group of 150 businesses(sample) is taken from the telephone listings(all the businesses in the listings is the population), hence option C is correct.

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b. the 68 businesses who returned surveys

Answer:

its C

Step-by-step explanation:

Answer: it would be B, here a picture for you to understand it

Step-by-step explanation: Hope you see the picture and hope this help

The angles are approximately: θa = 25.5°, θb = 25.5°, and θc = 11.9°. θa is the angle of refraction, θb is the angle of incidence, and θc is the angle of refraction when light exits the material.

To determine the angles θa, θb, and θc, we need to apply the laws of refraction.

θa: The angle of refraction when light passes from air (or vacuum) to a medium with an index of refraction is given by Snell's law:

n1sin(θ1) = n2sin(θ2)

In this case, the light ray is passing from air (n1 = 1) to the material with an index of refraction of n2 = 2. We are given the incident angle θ0 = 70.0°.

Applying Snell's law:

1sin(θ0) = 2sin(θa)

Simplifying and solving for θa:

sin(θa) = (1/2)*sin(70.0°)

θa = arcsin((1/2)*sin(70.0°))

θa ≈ 25.5°

Therefore, θa is approximately 25.5°.

θb: The angle of incidence when light passes from a medium with an index of refraction to air (or vacuum) is equal to the angle of refraction when light passes from air (or vacuum) to that medium. Therefore, θb is equal to θa.

θb ≈ 25.5°

θc: The angle of refraction when light passes from a medium with an index of refraction back to air (or vacuum) is given by Snell's law again:

n1sin(θ1) = n2sin(θ2)

In this case, the light is passing from the material with an index of refraction of n1 = 2 to air (n2 = 1). We can use the angle θb as the incident angle and solve for θc.

2sin(θb) = 1sin(θc)

Simplifying and solving for θc:

θc = arcsin((1/2)*sin(25.5°))

θc ≈ 11.9°

Therefore, θc is approximately 11.9°.

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--The given question is incomplete, the complete question is given below " A light ray passes through a rectangular slab of transparent material having index of refraction n=2, as shown in the figure (Figure 1) . The incident angle is θ0=70.0∘.

Determine θa.

Determine θb.

Determine θc. "--

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Solution

To write r > -10/3 on a number line,

Step 1: Draw a number line and include -10/3 on it

Step 2: Draw an arrow to the right with the small circle at its initial

Answer:

5 is the y-intercept

Step-by-step explanation:

The sine of the angle θ is given as follows:

sin(θ) = -16/65.

The trigonometric identity relating the cosine of an angle, along with the sine of the same angle, is given as follows:

sin²(θ) + cos²(θ) = 1.

In this problem, we have that cos(θ) = 63/65, hence the sine of θ is obtained as follows:

sin²(θ) + (63/65)² = 1

sin²(θ) = 1 - (63/65)²

sin(θ) = +/- sqrt(1 - (63/65)²)

sin(θ) = -16/65.

The sine has a negative sign as on the fourth quadrant, the sine is negative.

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Answer: 3x

Step-by-step explanation:

2x+1=3x

Answer:

In 11 seconds the elevator travels 363 feet

Step-by-step explanation:

Answer:

2x-6y=-24

2x=-24+6y

x=-24+6y÷2

x=-12+3y equation 1

x+(-5y)=-22

-12+3y-5y=-22

-13-2y=-22

-2y=-22+13

-2y=-9

y=-9÷2

y=4.5equation 2

putting value of equation 2 in equation 1

x=-12+3y

x=-12+3×4.5

x=-12+13.5

x=1.5 answer!!!

Answer:

98min

Step-by-step explanation:

16 cupcakes in 28mins

you need to find how many minutes it will take him to decorate one cupcake for that you do 28/16 which is 1.75

now to decorate 56 cupcakes, multiply 1.75x56

you get 98.

If Adrian continues at this pace, it will take him 98 minutes to decorate 56 cupcakes.

Hope this helps :)

It will take Adrian 98 minutes to decorate 56 cupcakes

First find out the number of minutes it takes him to decorate a single cupcake:

= Number of minutes / Number of cupcakes decorated

= 28 / 16

= 1.75 minutes per cupcake

If he had to decorate 56 cupcakes, the amount of time he would take is:

= Number of cupcakes to be decorated x Time taken per cupcake

= 56 x 1.75

= 98 minutes

It will therefore take him 98 minutes to decorate 56 cupcakes.

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It is proved in the answer that an exterior angle of the triangle equals the sum of two opposite interior angles.

If a triangle's side is created, the outside angle that results is equal to the product of the two opposite internal angles.

In the figure given below we can see:

∠BCD is the exterior angle of the triangle

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum property of a triangle)

∠BCA + ∠BCD = 180°(Linear pair)

From both equations we can say that:

∠ABC + ∠BAC + ∠BCA  = ∠BCA + ∠BCD

∠ABC + ∠BAC = ∠BCD

Hence Proved

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To obtain g(x) the graph of f(x) should be shifted in the right direction by 5 units

We can see and compare the graphs of f(x) and g(x) to see this visually

Since f(x) = x to the power of 2, so the graph of f(x) will be a parabola which will have center at the origin and opens upwards

The graph of g(x) will also be a parabola but it will have center at x = 5

So, we just need to shift the graph of f(x) by 5 units in right direction to obtain g(x)

In the equation of f(x), we just have to replace x with (x- 5) and we will get

g(x) = (x-5)^2

So, this will be the equation of parabola that's identical to f(x)

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We can start by setting the two functions equal to each other and solving for x:

f(x) = g(x)

x^2 = (x-5)^2

Expanding the right-hand side:

x^2 = x^2 - 10x + 25

Simplifying:

10x = 25

x = 2.5

So, the two functions intersect at x = 2.5. To shift f(x) to obtain g(x), we need to move it 5 units to the right, since the vertex of g(x) is at x = 5, which is 5 units to the right of the vertex of f(x) at x = 0.

Therefore, to obtain g(x) from f(x), we need to replace x with x-5:

g(x) = f(x-5) = (x-5) ^2

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Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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Answer:

5x-6

Step-by-step explanation:

Answer:

  y = 2·5^x

Step-by-step explanation:

Using the given points, we can solve for 'a' and 'b'.

  y = ab^x

  2 = ab^0 = a . . . . . substitute (0, 2) for (x, y)

__

  1250 = 2·b^4 . . . . substitute for 'a' and (4, 1250) for (x, y)

  625 = b^4 . . . . divide by 2

  5 = b . . . . . . . take the 4th root

The function is ...

  y = 2·5^x

____

Additional comment

There are two real and two imaginary 4th roots of 625. Only the positive real root is useful as the base in an exponential function like this.

Answer:

yes

Step-by-step explanation:

Answer:

I believe its (-6, 7)

Answer:

i hope this helps

Step-by-step explanation:

Answer:

-15/4

Step-by-step explanation:

Answer: Its - 15/4 or 05/12 but the person above me is correct

Step-by-step explanation:

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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To convert the FSM (Finite State Machine) to a controller using a state register and logic gates, follow these steps:
1. Identify the states of the FSM: Review the FSM you created for exercise 3.30 and list down all the states it contains.

2. Design the state register: Create a state register that can store the different states of the FSM. You can use flip-flops or any other suitable storage device.

3. Implement the logic gates: Use logic gates (such as AND, OR, and NOT gates) to implement the transitions between different states. Connect the outputs of the logic gates to the inputs of the state register.

4. Connect the state register to the FSM: Connect the outputs of the state register to the inputs of the FSM to control its behavior based on the current state.

5. Test and verify: Test the controller by simulating different inputs and checking if it transitions between the states correctly according to the desired behavior of the original FSM.

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Answer:

Your answer is

Perimeter = 18

Area= 20

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The volume of the square-based pyramid is 3888 units³. Your answer is option B. 3888 units³.

The formula to calculate the volume of a pyramid is V = (1/3)Bh,

Where B is the area of the base and h is the height.

In this case, the base is a square with edge length 9 units, so the area is B = 9² = 81 units².

The height is given as 48 units.
Plugging these values into the formula, we get:
To find the volume of a square-based pyramid, you can use the following formula:

V = (1/3) * base area * height.

In this case, the base edge is 9 units and the height is 48 units.

First, find the base area:

A = side * side = 9 * 9

= 81 square units.

Next, calculate the volume:

V = (1/3) * 81 * 48 = 3888 cubic units.
V = (1/3)(81)(48)
V = 1296 units³
Therefore, the volume of the pyramid is 1296 units³, which is option b.

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To prove that lim (n → ∞) |sn| = 0 implies lim (n → ∞) sn = 0, we will show that if the absolute value of a sequence converges to 0, then the sequence itself also converges to 0.

Let {sn} be a sequence such that lim (n → ∞) |sn| = 0. This means that for any ε > 0, there exists a positive integer N such that |sn| < ε for all n ≥ N. We want to show that lim (n → ∞) sn = 0.

Given ε > 0, we can choose the same N as before, such that |sn| < ε for all n ≥ N. Now, consider the difference between sn and 0, i.e., |sn - 0| = |sn|. Since |sn| < ε for all n ≥ N, it follows that |sn - 0| = |sn| < ε for all n ≥ N.

This shows that for any ε > 0, there exists a positive integer N such that |sn - 0| < ε for all n ≥ N, which is the definition of lim (n → ∞) sn = 0. Therefore, we have proven that if lim (n → ∞) |sn| = 0, then lim (n → ∞) sn = 0.

In conclusion, if the absolute value of a sequence converges to 0, then the sequence itself also converges to 0.

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