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The recursion tree is log2m and has log2m nodes .

A recursive algorithm calls itself with smaller input values and returns the result for the current input by carrying out basic operations on the returned value for the smaller input.

A iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for recurrence relations of types that occur in the analysis of many divide and conquer algorithms.

Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

Iterative: The pseudocode for this algorithm is as follows.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

The resulting number after the multiplication is i.n bits long. Thus

adding up all the multiplication cost we get

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

Recursive: The pseudocode for this algorithm is as follows:

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Applying the Master Theorem we can conclude that T(y) ∈ O(y2n2). The height

of the recursion tree is log2m and has log2m nodes.

Thus both the algorithms have the same worst case complexity.

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Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Thus both the algorithms have the same worst case complexity.

Answer: The symbol ⊕ is known as the XOR (Exclusive Or) operator.

Step-by-step explanation:

The symbol ⊕ is known as the XOR (Exclusive Or) operator. It is a logical operator that compares two binary digits or bits and returns a 1 if one of the bits is 1 but not both. It returns 0 if both bits are the same (either 0 or 1). It is commonly used in digital logic and computer science, particularly in the field of cryptography. In simple terms, it compares two bits and returns 1 if they are different and 0 if they are the same.

Answer:

No lol

Step-by-step explanation:

I actually hate maths..

Answer:

y= -3x+4

Step-by-step explanation:

Answer:

_________(ANSWER)_________

1.(C)

2.(D)

3.(B)

4.(A)

6.(D)

Explanation:

(BRAINLEIST PLEASE)❤☺️☻♨️♨️☻☺️❤

The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

  16 square units

Step-by-step explanation:

You want the area of the triangle bounded by the x- and y-axes and the line y = -2x +8.

The line has a y-intercept of +8, and an x-intercept of +4. This means the triangle height is 8 units and its base is 4 units.

The area is ...

  A = 1/2bh

  A = 1/2(4 units)(8 units) = 16 square units

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Note: Consider the below figure attached with this question.

Given:

The ordered pair(6,y) is on line AC.

To find:

The y of this ordered pair.

Solution:

From the below figure it is clear that endpoints of AC are A(-7,-4) and C(1,4). So, equation of AC is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-(-4)=\dfrac{4-(-4)}{1-(-7)}(x-(-7))\)

\(y+4=\dfrac{4+4}{1+7}(x+7)\)

\(y+4=\dfrac{8}{8}(x+7)\)

\(y+4=x+7\)

Subtracting 4 from both sides, we get

\(y+4-4=x+7-4\)

\(y=x+3\)

Thus, the equation of line AC is \(y=x+3\).

Put x=6 to find the y for the ordered pair (6,y).

\(y=6+3\)

\(y=9\)

Therefore, the value of y is 9.

Answer:

221.0 m

Step-by-step explanation:

First, find x using trigonometric ratio formula:

Reference angle = angle of depression = angle of elevation = 64°

Opposite side length = 142 m

Adjacent side length = x

Thus:

tan(64) = 142/x

x*tan(64) = 142

x = 142/tan(64)

x = 69.3 (nearest tenth)

Next, find distance from top of the hill to the buoy using Pythagorean Theorem.

Let the distance be y.

We would have:

y² = 142² + (69.3 + 100)²

y² = 20,164 + 28,662.49

y² = 48,826.49

y = √48,826.49

y = 221.0 m (nearest tenth)

The unknown lengths of the similar figures are:

r = 63 m

x = 45 m

Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.

Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:

Quadrilateral:

B/A  = C/B

15/5 = r/21

3 = r/21

r = 3 * 21

r = 63 m

Star:

18/4 = x/10

4.5 = x/10

x = 4.5 * 10

x = 45 m

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Answer:

a

Step-by-step explanation:

made a 100

Answer:

a = 38%, b = 3%

Step-by-step explanation:

got it correct.

Answer:70%

Step-by-step explanation:you have 7/10.SO u times the whole fraction by 10( 7 times 10 =70 and 10 times 10 =100) which means 70/100 so the percent is 70.

Hope it helps

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Answer:

105

Step-by-step explanation:

Answer:

the correct answer is -1/16 i believe

Answer:

The answer would be r = 1/v + 1/w

I hope this helps you! Have nice day! (:

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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To "decompose" is to separate or disassemble anything. In addition to geometric shapes, we can also decompose numbers.

A larger number is divided into smaller numbers by the process of decomposing.

fraction:

Decimals:

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Part A: The function is nonlinear.

Part B: We determined the function to be nonlinear because the corresponding y-values do not change by a constant rate as the x-values increase, indicating a lack of a linear relationship.

Part A: The given function is nonlinear.

Part B: To determine whether the function is linear or nonlinear, we need to examine the relationship between the x-values and the corresponding y-values in the table.

In a linear function, there is a constant rate of change between the x and y values.

This means that for every increase in x by a fixed amount, the corresponding y value will change by a constant amount.

If we look at the x-values in the given table (2, 3, 4), we can see that they are increasing by a fixed amount of 1 each time.

However, when we examine the corresponding y-values (20, 10, 40), we don't see a constant rate of change.

The y-values are not changing by the same amount for each increase in x.

For instance, when x increases from 2 to 3, the y-value decreases from 20 to 10.

This indicates a non-linear relationship as the change in y is not constant for each unit increase in x.

Additionally, when x increases from 3 to 4, the y-value jumps significantly from 10 to 40, which further confirms the nonlinear nature of the function.

Based on these observations, we can conclude that the given function is nonlinear.

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Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

31 + x + 4 + 3x + 9 = 180

4x + 44 = 180 ( subtract 44 from both sides )

4x = 136 ( divide both sides by 4 )

x = 34

Then

∠ S = x + 4 = 34 + 4 = 38°

∠ T = 3x + 9 = 3(34) + 9 = 102 + 9 = 111°

The value of a4 would be equal to -666.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that \(a_0=10\) and \(a_n+1=-5a_n\)

This is a recursive formula. So we can simply substitute in each value. For instance, a₂

Use the recursive definition repeatedly.

a2 = -5(6) +4 = -26

 a3 = -5(-26) +4 = 134

 a4 = -5(134) +4 = -666

Therefore, the value of a4 is -666

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The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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Answer:

The answer to 5 is 3 and the answer to 6 is -2

Step-by-step explanation:

-8=2x-14

add 14 to each side

6=2x

divide by 2

3=x

----------------------------

11x+13=-9

subtract 13 from both sides

11x=-22

divide each side by 11

x=-2

Answer:

5.x=3

6.x=-2

Step-by-step explanation:

you're welcome

Step-by-step explanation:

24 mins = 3 chores

x mins = 1 chore

cross multiplying

3x = 24

x = 8