Math Answers

1. a) Define differentiation and integration in calculus. Also write down the

differences between them. 

b) Write down some application of Calculus in CSE. 

c) Describe geometrical meaning of definite integral with figure.

How to draw a network diagram in mathematical foundations of computer science

Pepsi is running a sales proportion in which 12% of all bottles have a "FREE" logo under the cap. What is the probability that you find 2 free ones in a 6-pack? Round your answer to 3 decimal places.

a)     Suppose P (x, y) denotes the equation8, what will the truth values of the Propositions P (2,2), P (0,4).

An influenza vaccine is produced by two different companies. It is known that a vaccine

produced by company 1 is effective with probability 0:89, while a vaccine produced by

company 2 is effective with probability 0:93. We also know that company 1 supplies 40%

of the vaccines, while company 2 supplies 60% of the vaccines ordered by the government.

(i) What is the probability that a vaccine is effective, given that it was produced by company 2?

(ii) What is the probability that a randomly chosen vaccine from the government’s order

is not effective?

(iii) What is the probability that given a vaccine is not effective that it was produced by

company 1?

You have a deck of 52 playing cards

(i) How many different 8 card hands can be dealt?

(ii) What is the probability that a hand of 8 dealt randomly contains (exactly) 2 aces?

(iii) What is the probability that a hand of 7 dealt randomly will have 7 cards of the same suit?

for a particular function, dy/dx=8x-5. if it is known that when x= 2,y= 8,find y in terms of x

The local administration installed 3500 Incandescent bulbs as part of a new lighting system project. According to them, the bulbs are produced by several companies and have a burn time of 1060 hours on average. The distribution of the burning lives is close to normal. They discovered that the 350th light bulb had burned out after 822 hours of observation. What is the standard deviation of the burning lives of this set of lightbulbs? 

Let g(x) = {(ax^2-b) if x<2, (bx-a) if x>2}

Find a relationship between a and b (that is, solve for a in terms of b or vice versa) So that g(x) is continuous for all of x.

A swimming pool is to be drained for cleaning. The quantity of Q of water (in gallons) in the pool at any given time is a function of the amount of time t (in minutes) which has elapsed since the drain was opened. the function is: Q(t)= 10(20-t)³

find Q’(t)=

what is the rate of change of the quantity of water in the pool exactly 10 minutes after the drain is opened? (labeled units)

what is the average rate of change of the quantity of water during the first 10 minutes after the drain is open?

how long will it take to drain the pool completely? (labeled units)