TutorMe homepage
Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Riemann S.
Tutor for 3 years, Math Major, Applied Math Graduate Student
Tutor Satisfaction Guarantee
Calculus
TutorMe
Question:

Let R[x] be the set of polynomials with real coefficients. Define D: R[x] -> R[x] where D is the derivative operator, that is D sends the polynomial, as a function, to its derivative. Which of the following is true? A. D is 1-1 only B. D is onto only C. D is a bijection

Riemann S.
Answer:

If we take any polynomial from R[x], we can always find an antiderivative. That antiderivative, of course, is in R[x] as well. This makes D onto. However, D is not one-to-one because all the constant polynomials will be sent to the zero polynomial under D. Hence, the answer is B.

Statistics
TutorMe
Question:

Ash and his Pikachu are set to battle the next gym leader. However, the gym leader has a unique battle rule. The battle shall consist of five rounds. In each round, each trainer shall send out one Pokemon, and the round commences until a Pokemon faint. When the round ends, each trainer will need to withdraw his Pokemon and send out a new Pokemon. Each round, therefore, will be independent of the other rounds. The gym also has a unique way of awarding gym badges by giving Ash some badges equal to his net score at the end of all five rounds. Ash's net score will be equal to the number of rounds he will win minus the number of rounds he will lose. Ash will not receive any badge if his net score is zero or negative. Assuming that around will never result in a tie and that the probability that Ash will win around is fixed at 2/3. What is the probability that Ash will receive EXACTLY three badges?

Riemann S.
Answer:

Ash will win three badges if he wins four rounds and loses 1 round. With each round having a constant probability of success, and all rounds independent of one another, the problem, therefore, can be modeled by a binomial distribution with n=5 and p=2/3. P(X=4) = 5C4 (2/3)^4 (1/3) = 80/243 Or without referring to the Binomial distribution, we can think of it this way: We want Ash to win four rounds out of the 5. It doesn’t matter which rounds he will win as long as he wins 4. We, therefore, choose 4 of the rounds which Ash can win. This can be done in 5C4 = 5 ways. We are now left with the probability that Ash will indeed win 4 of the rounds. Well, he needs to win four but lose 1. Since the probability of him winning is 2/3 and losing is 1/3, this probability is given by (2/3)^4 *(1/3)^1 = 16/243. Thus, the desired probability is 5(16/243)= = 80/243.

Algebra
TutorMe
Question:

Solve: 2(3x+4)^2 -7(3x+4) = 9.

Riemann S.
Answer:

Just let 3x+4 = y first so that the equation becomes 2y^2 - 7y =9 Now this looks familiar, right? it is a quadratic polynomial equation Now if we "transpose" 9 to the left-hand side we have: 2y^2 -7y -9 =0 We can factor this as (2y-9)(y+1) = 0 and get 2y=9 or y =-1 These yield possible values of y to be y=9/2 and y = -1 Now since 3x+4=y we just plug in our computed y's On one hand, if y =9/2, then 3x+4=9/2 => 3x = 1/2 => x =1/6. On the other hand, if y = -1, 3x+4 = -1 => 3x = -5 => x = -5/3. so the solutions for x are 1/6 and -5/3.

Send a message explaining your
needs and Riemann will reply soon.
Contact Riemann
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.