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2 years ago

Consider a tree T storing 100,000 entries. What is the worst-case height of T in the following cases?

Mathematics

1 answer:

Darina [25.2K]2 years ago

6 0

Answer:

Step-by-step explanation:

a.) The worst-case height of an AVL tree or red-black tree with 100,000 entries is 2 log 100, 000.

b.) A (2, 4) tree storing these same number of entries would have a worst-case height of log 100, 000.

c.) A red-black tree with 100,000 entries is 2 log 100, 000

d.) The worst-case height of T is 100,000.

e.) A binary search tree storing such a set would have a worst-case height of 100,000.

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A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle is at the point (3,4), dx/dt

yaroslaw [1]

Answer:

$\displaystyle y'=-\frac{9}{2}$

Step-by-step explanation:

Differentiation

We have a relationship between x and y as follows:

$x^2+y^2=25$

Both variables depend on time t for t≥0.

Differentiating with respect to time:

$(x^2)'+(y^2)'=(25)'$

Applying the derivative of a power function:

$2xx'+2yy'=0$

Recall the derivative of a constant is 0.

Dividing by 2:

$xx'+yy'=0$

Solving for y':

$\displaystyle y'=-\frac{xx'}{y}$

At some specific time, we have:

x=3, y=4, dx/dt = x' = 6. Substituting:

$\displaystyle y'=-\frac{3\cdot 6}{4}$

Operating:

$\displaystyle y'=-\frac{18}{4}$

Simplifying:

$\mathbf{\displaystyle y'=-\frac{9}{2}}$

8 0

2 years ago

Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon? A hexagon is shown. A triangle with a 60

damaskus [11]

Answer:

The area of the hexagon is A. 96√3 cm²

Step-by-step explanation:

Let's recall the formula of the area of an hexagon, this way:

Area = (3√3/2) * s²

Area = (3√3/2) * 8²

Area = (3√3/2) * 64

Area = 192√3/2

Area = 96√3 cm²

The area of the hexagon is A. 96√3 cm²

7 0

2 years ago

The high temperature for the day was 20 degrees above zero, but at night, the temperature fell to 15 degrees below zero. What wa

erastovalidia [21]

35 degree swing. 20 to -15 is 35

4 0

2 years ago

The histogram below shows the estimated monthly salaries of company employees with different years of experience.

skad [1K]

From the Histogram displaying the the estimated monthly salaries of company employees with different years of experience, the graph might be misleading given that:
The scale on the y-axis overemphasizes the difference in salaries between different experience levels.

It might not be the case always that salary increment is proportional to experience, this might not fit all the cases.

8 0

2 years ago

Read 2 more answers

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal. During one

Triss [41]

Answer:

0.82 = 82% probability that at least one party will not order drinks

Step-by-step explanation:

For each party, there are only two possible outcomes. Either they will order drinks with their meal, or they will not. The probability of a party ordering drinks with their meal is independent of other parties. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal.

This means that $p = 0.75$

During one hour, Ryan served 6 parties. Assuming that each party is equally likely to order drinks, what is the probability that at least one party will not order drinks?

6 parties, so n = 6.

Either all parties will order drinks, or at least one will not. The sum of the probabilities of these events is decimal 1. So

$P(X = 6) + P(X < 6) = 1$