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The given recurrence relation is t(n) = 2t(n/2) + n. Its solution can be found using the Master Theorem, which is applicable to recurrence relations of the form T(n) = aT(n/b) + f(n).

Let's provide a step-by-step explanation for solving the given recurrence relation, t(n) = 2t(n/2) + n, using the Master Theorem:

The given recurrence relation is of the form t(n) = a * t(n/b) + f(n), where a = 2, b = 2, and f(n) = n.

To find the solution using the Master Theorem, we compare f(n) with n^(log_b(a)), which is n^(log_2(2)) = n.

In this case, f(n) = n and n^(log_b(a)) = n^(log_2(2)) = n^1 = n. Since f(n) is of the same order as n^(log_b(a)), we fall into case 2 of the Master Theorem.

According to case 2, if f(n) = Θ(n^c * log^k(n)), where c = log_b(a), then the solution to the recurrence relation is t(n) = Θ(n^c * log^(k+1)(n)).

In our case, c = log_2(2) = 1 and k = 0. Therefore, the solution to the recurrence relation t(n) = 2t(n/2) + n is t(n) = Θ(n^1 * log^(0+1)(n)) = Θ(n * log(n)).

Hence, the correct solution to the given recurrence relation is t(n) = Θ(n * log(n)).

This recurrence relation represents the time complexity of certain divide-and-conquer algorithms, such as Merge Sort. Merge Sort works by recursively dividing the input array into two equal halves, sorting them, and then merging the sorted halves. The time complexity of Merge Sort is indeed Θ(n * log(n)), matching the solution to the given recurrence relation.

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From set theory, A and B: {4, 6} A or B: {2, 3, 4, 5, 6, 8} B's complement is 1, 2, 7, and 8.

Basic set theory describes these various kinds of sets as follows: Finite set: There are only a finite number of elements. A set with an infinite number of elements. A set that is empty has no elements. A singleton set consists of just one element.

The elements that appear in both A and B at the same time are referred to as A and B.

From 1 to 8, the even numbers are 2, 4, 6, and 8.

The numbers 3, 4, 5, and 6 are in that order.

Look for the components that are the same in both sets.

A and B: {4, 6}

The union of the two sets is either A or B.

Combine the components from both sets.

A or B: {2, 3, 4, 5, 6, 8}

All the components that are absent from B make up its complement.

Except for the event elements, write all of the sample space's components.

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My answer is 5.2.30am I am not Paris Paris I'm thankful to 6.30am I am not

Answer: 20.51%

Step-by-step explanation: This question uses the binomial distribution.

210/1024=105/512≈0.2051

The triangles are classified as follows

1. not similar

2. similar by Pythagoras theorem

3.  similar by Pythagoras theorem

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that

The constant of proportion for the second is 1.4 and 2 for the third figure

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Answer:

B. -2/5

Step-by-step explanation:

Use the "rise over run method"

Do this by finding two points on the graph, then finding the distance between the two points. First find the vertical distance, then the horizontal. The direction represents whether the slope will be negative or positive. When it goes up, it'll be positive, down=negative. Right=positive, left=negative. Two negatives make a positive, but one positive and one negative make a negative.

The calculated area of the cross-section is 14 square inches

from the question, we have the following parameters that can be used in our computation:

The prism (see attachment 1)

When a vertical plane intersects the vertex and the shorter edge of the base, the shape formed is a triangle with the following dimensions

Base = 7 inches

Height = 4 inches

See attachment 2

So, we have

Area = 1/2 * 7 * 4

Evaluate

Area = 14

Hence, the area of the cross-section is 14 square inches

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Answer:

x=6/5

Step-by-step explanation:

6=2x+3x

5x=6

x=6/5

Answer:

false

Step-by-step explanation:

The left side equals 0.01

The right side equals 0.4

The two sides are not equal. This is a false equation.

Answer:0.01=0.0001

Step-by-step explanation:

Answer:

4 \(\sqrt5\)

Step-by-step explanation:

Use Pythagorean theorem to get c^2 for the hypotenuse, which is equal to \(\sqrt80\). You then simplify to get the simplest radical form by \(\sqrt80\) = \(\sqrt{8*10} = \sqrt{4*2*5*2} = \sqrt{16*5} = 4\sqrt{5}\)

To find the standard matrix for the linear transformation T: T(x, y) = (x + 6y, x - 4y), we need to determine the image of the standard basis vectors (1, 0) and (0, 1) under T.

Let's start with the standard basis vector (1, 0):

T(1, 0) = (1 + 6(0), 1 - 4(0)) = (1, 1)

The image of (1, 0) is (1, 1). Therefore, the first column of the standard matrix will be (1, 1).

Next, let's consider the standard basis vector (0, 1):

T(0, 1) = (0 + 6(1), 0 - 4(1)) = (6, -4)

The image of (0, 1) is (6, -4). Therefore, the second column of the standard matrix will be (6, -4).

Putting it all together, the standard matrix for the linear transformation T is:

| 1   6 |

| 1  -4 |

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Answer:

275 bicycles

Step-by-step explanation:

We are given the average cost per bicycle as;

C(x) = 0.2x² - 1.1x + 10.592

We will solve this by finding the derivative of the C(x) function which will give us the instantaneous slope. Thereafter, we will find the extremas which will occur when the instantaneous slope is equal to 0.

Thus, derivative of C(x) is;

C'(x) = 0.4x - 1.1

Equating to zero, we can find the extremas.

Thus;

0.4x - 1.1 = 0

x = 1.1/0.4

x = 2.75

To check if this is minimum of maximum, we will find the second derivative of C(x)

Thus;

C''(x) = 0.4

Thus is a positive value, and so it means the critical point is a minimum.

Thus, X = 2.75

We were told x is in hundreds of bicycles. Thus, X = 2.75 × 100 = 275 bikes

Question:

What is the m∠ACB in the circle shown below?

Answer:

45

Step-by-step explanation:

So we know it is less than a right angle and it is not a obtuse angle it is less than 90 degrees. 45 is less, 90 is equal(not what we are looking for) , 120, is greater, and 180 is greater which leaves us to our answer 45.

The area of the base of the triangular prism is 48 square meters. Then the correct option is B.

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.

A triangular prism has a height of 6 meters and a triangular base with the following dimensions.

The figure is shown below.

Then the area of the base of the triangular prism will be

\(\rm Area = \dfrac{1}{2} \times 16 \times 6\\\\Area = 48\)

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Answer: b. 1923

Step-by-step explanation:

Answer:

58 degrees

Step-by-step explanation:

"I" and "K" has the degree of 58. "G" and "J" has a similar measurenmet (acute angle). So, I assume that "X" should be 58 degrees.

Answer:

to show the changes in private school enrollment

Answer:

E) \(x = 4\:\:y=2\sqrt3\)

Step-by-step explanation:

\(cos \: 60 \degree = \frac{2}{x} \\ \\ \frac{1}{2} = \frac{2}{x} \\ \\ \bold{ \purple{ \boxed{ \bold{x = 4}}}} \\ \\ tan \: 60 \degree = \frac{y}{2} \\ \\ \sqrt{3} = \frac{y}{2} \\ \\ \bold{ \red{ \boxed{ \bold{y = 2 \sqrt{3} }}}} \\ \\ \)

Answer:

x = -12       x = -5

Step-by-step explanation:

-7x-60=x^2+10x

Add 7x to each side

-60=x^2+10x+7x

-60=x^2+17x

Add 60 to each side

0 = x^2+17x+60

Factor

What 2 numbers multiply to 60 and add to 17

12*5 = 60

12+5 = 17

0 = (x+12) (x+5)

Using the zero product property

x+12 = 0   x+5 =0

x = -12       x = -5

Answer:

-12, and -5

Step-by-step explanation:

We first need to turn this equation into a quadratic. To do so, we set one side to zero. Our new equation is now

x^2+17x+60=0

By using the factoring the equation, we can see that this can be made into

(x+12)(x+5)

Our roots are now -12 and -5.

Hope this helped!

There are 8 cans will be needed to cover 208 m² of wall space.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Five cans of paint will cover 130 m² of wall space.

Now, Number of cans to cover 208 m² of wall space is,

⇒ 5 × 208 / 130

⇒ 8

Thus, There are 8 cans will be needed to cover 208 m² of wall space.

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Answer:

Standard form answer should be -33.

Sincerely sorry if im incorrect

Answer:

56x-24y = 33

Step-by-step explanation:

The complexity, reliability, and context of the evidence collected are some of the reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.

There are several reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.

Firstly, different types of evidence require different analytical techniques, as they have varying degrees of complexity. For example, analyzing DNA evidence requires a different set of analytical tools compared to analyzing physical evidence like fingerprints or footprints.

Secondly, the reliability of the evidence also plays a significant role in the analytical scheme. Some types of evidence may be more subjective than others, and the interpretation of the results may be open to bias or misinterpretation. In such cases, a simple analytical scheme may not provide accurate or reliable results.

Finally, the context in which the evidence is collected also plays a crucial role in determining the analytical scheme. The location, timing, and circumstances of the evidence collection may affect the reliability and accuracy of the results. Therefore, a simple analytical scheme may not be able to accommodate all the variables and nuances of the evidence collected in different contexts.

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Answer:

x is all real numbers

Step-by-step explanation:

The domain is the input to the function.  It is the values that x can take.

For this function, x can be any real value

(a) The lower bound of the confidence interval is 7.917 minutes.

(b) The upper bound of the confidence interval is 8.483 minutes.

(c) The margin of error is 0.283 minutes.

(a) The point estimate of the population mean is 8.2 minutes.

To calculate the lower bound of the 90% confidence interval, we use the formula: lower bound = point estimate - z* (standard error), where z* is the z-score for the 90% confidence level, which is 1.645, and the standard error is equal to the population standard deviation divided by the square root of the sample size, i.e., 2.2 / sqrt(200) = 0.156.

Substituting these values in the formula, we get the lower bound as 8.2 - 1.645 * 0.156 = 7.917 minutes.

(b) To calculate the upper bound of the 90% confidence interval, we use the same formula: upper bound = point estimate + z* (standard error). Substituting the values, we get the upper bound as 8.2 + 1.645 * 0.156 = 8.483 minutes.

(c) The margin of error is the difference between the point estimate and the upper or lower bound of the confidence interval. In this case, it is equal to half the width of the confidence interval, which is (8.483 - 7.917) / 2 = 0.283 minutes.

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Answer:

Simplified expression for the height of the rectangular prism is (w+1)

Step-by-step explanation:

Volume of rectangular prism = length x width x height = 2w^{3} + 7w^{2} + 5w

Length = 2w+5 Width = w and Height = h (Let)

=> 2w^{3} + 7w^{2} + 5w = (2w+5)wh

=> 2w^{2} + 7w + 5 = (2w+5)h

=> (2w+5)(w+1)=(2w+5)h

=> h = (w+1)

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Answer:

Simplified expression for the height of the rectangular prism is (w+1)

Step-by-step explanation:

Volume of rectangular prism = length x width x height = 2w^{3} + 7w^{2} + 5w

Length = 2w+5 Width = w and Height = h (Let)

=> 2w^{3} + 7w^{2} + 5w = (2w+5)wh

=> 2w^{2} + 7w + 5 = (2w+5)h

=> (2w+5)(w+1)=(2w+5)h

=> h = (w+1)

Answer:

72 square inches

Step-by-step explanation:

The surface area is the sum of all the sides' areas.

**I am assuming the pyramid is a square pyramid based on observation.

There is one 4 by 4 square: area = \(4^2=16\)

There are 4 congruent triangles with height 7 and base 4: area of a single triangle = 1/2 * b * h; \(\frac{7*4}{2}=14\)

14 * 4 = 56

Add 56 and 16 = 72

Answer:

72 square inches

Step-by-step explanation:

The surface area is the sum of all the sides' areas.

**I am assuming the pyramid is a square pyramid based on observation.

There is one 4 by 4 square: area =

There are 4 congruent triangles with height 7 and base 4: area of a single triangle = 1/2 * b * h;

14 * 4 = 56

Add 56 and 16 = 72

Step-by-step explanation:

In the following question, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

To find the surface area of the scratching post, we need to add up the surface areas of all the sides.

The scratching post has a rectangular prism shape with dimensions of 10 cm x 10 cm x 90 cm. The bottom is also a 10 cm x 10 cm square.

So the surface area of the post, including the bottom, is:

2(10 cm x 10 cm) + 2(10 cm x 90 cm) + 2(10 cm x 10 cm) = 200 cm^2 + 1800 cm^2 + 200 cm^2 = 2200 cm^2

Therefore, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

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Answer: B) 20.25

Step-by-step explanation:

22.5% = 0.225

22.5% of 90 = 0.225 * 90 = 20.25

Hope it helps and lmk if you need more info <3 :D

Answer:

B. 20.25

Step-by-step explanation:

22.5 percent *90 =

(22.5:100)*90 =

(22.5*90):100 =

2025:100 = 20.25