Provide a tight bound for the running time of finding the largest element in a binary min-heap with n elements?

Answers

Answer 1

The tight bound for finding the largest element in a binary min-heap with n elements is O(log n).

To find the largest element in a binary min-heap, we start at the root node which contains the smallest element. From there, we compare the left and right child nodes and choose the larger of the two. We continue this process until we reach a leaf node, which is the largest element in the heap.

Since the binary min-heap has a complete binary tree structure, the height of the tree is O(log n). Therefore, the number of comparisons we need to make to find the largest element is proportional to the height of the tree, which is O(log n).

Therefore, the tight bound for finding the largest element in a binary min-heap with n elements is O(log n).

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Related Questions

Write
3
6
in lowest terms.

Answers

Answer:

1/2

Step-by-step explanation:

3 is half of 6 so the answer would be 1/2.

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 13π 15 cos − π 5 − sin 13π 15 sin − π 5 Find its exact value.

Answers

As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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PLEASE HELPPPPPPPPPPPPPP

PLEASE HELPPPPPPPPPPPPPP

Answers

Answer:

The answer is 18

Step-by-step explanation:

4050/225 = 18

Therefore 4050/18 = 225

A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 20.

Answers

The sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

The formula for sample mean is given by,

Sample Mean \((X)= (x1+x2+x3+...+xn) / n\)

Where x1, x2, x3,...,xn are individual observations and n is the number of observations.

In this case, the sample mean (X) is given as 20 and the number of observations (n) is 10.

Therefore, the formula can be written as:

\(X = (x1+x2+x3+...+x10) / 10\)

Since the population standard deviation (σ) is given as 5, the standard deviation of the sample (s) can be calculated using the formula:

s = σ/√n

Where n is the number of observations.

Therefore, in this case, the standard deviation of the sample (s) is calculated as:

s = 5/√10

s = 2.23

Thus, the sample mean (X) of 10 observations selected from a normal population having population standard deviation (σ) of 5 is 20 with the standard deviation of the sample (s) being 2.23.

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how to calculate cube root without using prime factorization? and how to calculate ³√60? or something else that has a decimal result?​

Answers

The cube root of 60 is 3.87 approximately.

Step by step solution:

We can calculate the cube root by Halley's method:

The  formula is \(\sqrt[3]{a} = x ((x^{3} + 2a)/(2x^{3} + a))\)

where,

a = number whose cube root is being calculated

x = integer guess of its cube root.

Here a = 60,

Suppose x as 3

[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 60]

⇒ x = 3

Therefore,

∛60 = 3 (3³ + 2 × 60)/(2 × 3³ + 60)) = 3.87

⇒ ∛60 ≈ 3.87

Therefore, the cube root of 60 is 3.87 approximately.

Here ,  ∛60 is irrational because it cannot be expressed in the form of p/q where q ≠ 0.

Therefore, the value of the cube root of 60 is an irrational number.

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please help and answer in simple terms.

How are rational exponents and radicals related? Summarize how to rewrite a rational power as a radical term using an example of your own.

Answers

Rational exponents are exponents written in the form of a fraction.

A rational power can be rewritten as a radical in the following way: the bottom of the rational exponent is the root, while the top of the rational exponent is the new exponent on the radical.

Example: X^(1/2)= √X

a ramp 27ft long rises to a platform. the bottom of the platform is 16ft from the foot of the ramp. find , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.

Answers

Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.


What is the angle of elevation?

The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.

We need to find the angle of elevation of the ramp.

The angle of elevation of the ramp is the angle made by the ramp with the horizontal.

Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.

We need to find the angle ABD.

Consider right-angled ΔABC In right-angled ΔABC,

we have:

tan⁻¹ (BC / AB)

θ  = tan⁻¹ (27 / 16)

θ ≈ 59.35°

Hence, the angle of elevation of the ramp is approximately 59.35°.

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Four times the sum of 5 and some number is 20. What is the number?

Answers

This is the answer to your problem

Four times the sum of 5 and some number is 20. What is the number?

A plane can carry 360 passengers. On a particular day, there are 240 passengers on the plane. Identify the correct inequality and the solution to show how many more passengers the plane can carry?

Answers

Answer:

p + 240 ≤ 360; p ≤ 120

Step-by-step explanation:

The inequality that shows the number of more passengers to carry by plane is 240 + x = 360.

The number of more passengers is 120.

What is inequality?

It is a statement of an order relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Number of passengers in a plane = 360

Number of passengers in a day = 240

The inequality represents the number of more passengers that can carry:

240 + x = 360

Where x is the number of more passengers.

Find x.

240 + x = 360

Subtract 240 on both sides.

240 + x - 240 = 360 - 240

x = 120

Thus,

The inequality that shows the number of more passengers to carry by plane is 240 + x = 360.

The number of more passengers is 120.

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What is the midpoint of the segment shown below?

What is the midpoint of the segment shown below?

Answers

Answer:

It is C (4,3). Hope it helps.

Answer:

C. (4,3)

Step-by-step explanation:

To find the midpoint you must individually add the X's and the Y's and divide by 2. For example in this case, -2+10=8 divide by 2 and get 4. Then 3+3=6 divide by 2 is 3. It's that simple.

9. Determine whether the following graph is a function or a relation.

9. Determine whether the following graph is a function or a relation.

Answers

Answer: Relation

Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts

I need help pleassse

I need help pleassse

Answers

Answer:

210 ml

Step-by-step explanation:

In △ABC,a=14, b=17, and c=22. Find m∠B

Answers

Answer:

Step-by-step explanation:

In ABC,a=14, b=17, and c=22. Find mB

The class has 25 regular participants. Each participant uses 4 weights. Aaliyah writes the expression 4(25 – n) to represent the number of weights needed if n regular participants do not come to class. The gym manager represents the number of weights needed with the expression 100 – 4n. What information does each expression tell you? Explain your reasoning. ​

Answers

The first expression, 4(25 – n), tells us the number of weights needed if n regular participants do not come to class.

This is because each regular participant uses 4 weights, and if n regular participants do not come to class, then the number of regular participants present would be 25 – n.

Multiplying this by 4 gives us the total number of weights needed.
The second expression, 100 – 4n, represents the number of weights needed according to the gym manager. This expression tells us that the gym manager has calculated the number of weights needed based on the number of regular participants who are absent, which is represented by n. The expression subtracts 4n from 100 because each regular participant uses 4 weights.
In summary, both expressions represent the number of weights needed for the class based on the number of regular participants who do not come to class. Aaliyah's expression uses 4(25 – n) to calculate the number of weights needed, while the gym manager's expression uses 100 – 4n to represent the same information.

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Please help with this 25 points

Please help with this 25 points

Answers

Answer:

25 x 13 = 325

Bat = 20

Pumpkin = 5

Witch = 10

Leaf = 50

Ghost = 60

Step-by-step explanation: hope this helps :)

Can someone please check my answer for this function???

Can someone please check my answer for this function???

Answers

Answer:

You're wrong, it's the bottom left

Step-by-step explanation:

x^2-49 is a difference of squares so it factors into (x+7)(x-7) which obviously cancels out with the denominator leaving x-7 left. This is the line you should graph, but keep in that x+7 is still in the denominator so x cannot be equal to -7 which means that this point should be be on the line which leaves the answer to be the one on the bottom left.

2(x + 4) < 4x - 6 smallest integer

Answers

Answer:

The smallest integer is 8

Step-by-step explanation:

2( x + 4 ) < 4x - 6

4x - 6 > 2x + 8

2x > 14

x > 7

The smallest integer is 8

which statement best describes the graph of the system of equations? x-y=1, y-x=1

Answers

Answer:

             Parallel lines

Step-by-step explanation:

x - y = 1                                       y - x = 1

- y = -x + 1                                   y = x + 1  ⇒ m₂ = 1, b₂ = 1

÷(-1)     ÷(-1)

y = x - 1 ⇒ m₁ = 1, b₁ = -1

m₁ = m₂   and   b₁ ≠ b₂ means that the lines described by these equations are parallel

Answer:

The lines are parallel

Step-by-step explanation:

correct on edge

the curve c, which goes along y = x2 from the point (0, 0) to the point (2, 4), then in a straight line from (2, 4) to (0, 4), and then along the y-axis back to (0, 0)

Answers

The total length of the curve is:

L = L₁ + L₂ + L₃ = 2.841 + 2 + 4 = 8.841.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

To find the length of the curve, we need to break it into its three segments and find the length of each segment separately.

Segment 1: y = x² from (0,0) to (2,4)

The length of this segment can be found using the arc length formula for a curve y = f(x) from x = a to x = b:

L = ∫[a,b] √[1 + (dy/dx)²] dx

In this case, f(x) = x², so dy/dx = 2x. Thus, the length of this segment is:

L1 = ∫[0,2] √[1 + (2x)²] dx ≈ 2.841

Segment 2: Straight line from (2,4) to (0,4)

The length of this segment is simply the distance between the two points:

L₂ = √[(0-2)² + (4-4)²] = 2

Segment 3: y-axis from (0,4) to (0,0)

The length of this segment is simply the distance between the two points:

L3 = √[(0-0)² + (4-0)²] = 4

Therefore, the total length of the curve is:

L = L₁ + L₂ + L₃ = 2.841 + 2 + 4 = 8.841

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find a power series representation for the function. f(x) = x^4 tan−1(x^3)
[infinity]
f(x) = ∑ (((-1)^n+1 (x)^6n+1)/(2n1-1))
n = 0
Determine the radius of convergence, R.

Answers

Therefore, the radius of convergence for the power series representation of f(x) is R = 1.

To find the power series representation of the function f(x) = x^4 * tan^(-1)(x^3), we can start by expanding the arctan function using its known power series representation:

arctan(x) = ∑((-1)^(n) * (x)^(2n+1))/(2n+1)

n = 0

We can substitute x^3 into the power series representation of arctan(x):

arctan(x^3) = ∑((-1)^(n) * (x^3)^(2n+1))/(2n+1)

n = 0

Simplifying the expression:

arctan(x^3) = ∑((-1)^(n) * (x)^(6n+3))/(2n+1)

n = 0

Now, we multiply the power series representation of arctan(x^3) by x^4 to obtain the power series representation of f(x):

f(x) = x^4 * arctan(x^3) = ∑((-1)^(n) * (x)^(6n+7))/(2n+1)

n = 0

Therefore, the power series representation of the function f(x) = x^4 * tan^(-1)(x^3) is:

f(x) = ∑((-1)^(n) * (x)^(6n+7))/(2n+1)

n = 0

To determine the radius of convergence, R, we can use the ratio test. The ratio test states that if we have a power series ∑(a_n * (x - c)^n), then the radius of convergence R is given by:

1/R = lim (|a_(n+1)/a_n|)

n -> ∞

In this case, our power series is ∑((-1)^(n) * (x)^(6n+7))/(2n+1). We can apply the ratio test to find the radius of convergence:

|((-1)^(n+1) * (x)^(6(n+1)+7))/(2(n+1)+1)| / |((-1)^(n) * (x)^(6n+7))/(2n+1)|

= |(-1) * (x^6) * (2n+1) / ((2n+3) * x^6)|

= |(-1) * (2n+1) / (2n+3)|

= |-2n-1 / 2n+3|

Taking the limit as n approaches infinity:

lim |-2n-1 / 2n+3| = |-2 / 2|

= 1

To find the radius of convergence R, we take the reciprocal of the above limit:

1/R = 1

R = 1

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. The top horizontal edge of the rectangle measures 17 centimeters, the left vertical edge of the rectangle measures 22 centimeters, and the bottom horizontal edge measures 17 centimeters. The left vertical leg is on the right edge of the rectangle, with v Calculate the area of the composite figure, which is not drawn to scale.

Answers

The area of a shape is the amount of space the shape occupies

The area of the composite figure is 488 square meters

How to calculate the area of the composite figure

The area of the composite figure is the area of the rectangle added to the area of the triangle

So, we have:

\(Area = 17 * 22 + 0.5 * 19 * (22 - 10)\)

Evaluate

\(Area = 488\)

Hence, the area of the composite figure is 488 square meters

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use long division to solve 514/28.

Answers

The division for 514 / 28 is 18 remainder 10.

What is division?

Long Division is a method for dividing large numbers, that breaks the division problem into multiple steps

Step 1: Here, the digits to first use is 51. This means 51 divided by 28 will give 1.

Step 2: Subtract 28 from 51 and this is 23. Bring the third digit of the dividend down and place it beside 23. This will be 234.

Step 3: Now, 234 divided by 28 will be 18.

Step 4: Multiply 18 by 28 and subtract the value. The remainder will be 10.

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Solve for x in this equation. 24 + 5x + 6 = -10

Answers

let's solve for x :

24 + 5x + 6 = -10

30 + 5x = -10

5x = -10 - 30

5x = -40

x = -40 ÷ 5

x = -8

Answer: x = -8

Step-by-step explanation: 24 + 5x + 6 = -10

1. Add (24+6=30)

2. (5x+30=-10)

3. Subtract 30 from both sides, cross out 30-30 and subtract (-10-30)

4. 5x-40

5. Divide by 5

6. -40/5= -8

I need help who can help me ??

I need help who can help me ??

Answers

Answer:

Step-by-step explanation:

10

Devon has 11 more than twice as many customers as when
he started selling custom baseball hats. He now has 73
customers. How many customers did he have when he
started?

Answers

Answer: 6

He started with 6 costumers

A company operates two plants which manufacture the same item and whose total cost functions areC1=6.7+0.03(q1)² and C2=7.9+0.04(q2)²,where q1 and q2 are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q=q1+q2, is related to the price, p, byp=40−0.04q.How much should each plant produce in order to maximize the company's profit? Q1= Q2=

Answers

Each plant should produce 576.92 units and 384.61 units respectively to maximize the company's profit.

To maximize the company's profit, we need to find the quantity that maximizes the difference between the total revenue and the total cost. The total revenue is given by:

TR = pq

= (40 - 0.04q)(q1 + q2)

= 40q1 + 40q2 - 0.04\(q1^2\)- 0.04\(q2^2\) - 0.04q1q2

The total cost is given by:

TC = C1 + C2

\(= 6.7 + 0.03q1^2 + 7.9 + 0.04q2^2= 14.6 + 0.03q1^2 + 0.04q2^2\)

The profit is given by:

π = TR - TC

= \(40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2\)

Simplifying, we get:

π = \(40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2\)

= \(-0.03q1^2 - 0.04q2^2 - 0.04q1q2 + 40q1 + 40q2 - 14.6\)

To maximize profit, we need to take the partial derivatives of the profit function with respect to q1 and q2 and set them equal to zero:

∂π/∂q1 = -0.06q1 - 0.04q2 + 40 = 0

∂π/∂q2 = -0.08q2 - 0.04q1 + 40 = 0

Solving these equations simultaneously, we get:

q1 = 576.92

q2 = 384.61

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la relación de dos varillas es 3/4 y la suma de sus longitudes es de 28cm¿cuánto mide cada una de las varillas?

Answers

Answer:

its 6

Step-by-step explanation:

what is the value of f(x) = 2•2 ^x for f(-2)?

Answers

Answer:

Sorry icant help

Step-by-step explanation:

i never did this before

Determine if Ginny factored correctly. If not, explain
where she made an error.

Answers

Answer:

The answer is A

Step-by-step explanation:

Please help
graph x<2.

Please help graph x&lt;2.

Answers

Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

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