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

Answer:

1/2

Step-by-step explanation:

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

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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Answer:

The answer is 18

Step-by-step explanation:

4050/225 = 18

Therefore 4050/18 = 225

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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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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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

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

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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This is the answer to your problem

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.

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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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.

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

Answer:

210 ml

Step-by-step explanation:

Answer:

Step-by-step explanation:

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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Answer:

25 x 13 = 325

Bat = 20

Pumpkin = 5

Witch = 10

Leaf = 50

Ghost = 60

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

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.

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

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

The area of the composite figure is 488 square meters

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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The division for 514 / 28 is 18 remainder 10.

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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let's solve for x :

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

Answer:

Step-by-step explanation:

10

Answer: 6

He started with 6 costumers

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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Answer:

its 6

Step-by-step explanation:

Answer:

Sorry icant help

Step-by-step explanation:

i never did this before

Answer:

The answer is A

Step-by-step explanation:

Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct