Math Answers

Using the Cauchy –Riemann equations verify the following is analytic or not

i) 𝑥^2 − 𝑦^2 + 2𝑖𝑥𝑦

ii) 𝑥^2 + 𝑦^2 − 2𝑖𝑥𝑦

Construct a truth table (truth matrix) for each of these compound proposition

1. p ∧ ~q
2. p → ~q
3. ( p ∨ q ) → ( p ∧ q)
4. ( p ∨ q ) → r
5. ( p ∨ q )∧ ~r

by using truth table (truth matrix), show that each statement is a tautology, contradictory or a contingent statement.

1. ~p ∧ q
2. ~(p ∨ q) → q
3. ~(~p ∧ q) ∨ q
4. ~p → (p → q)
5. ~p → (p ∨ q)

the sum of two numbers is 4. find the minimum value of the sum of their cubes.

You play a game with two six-sided dice. If you roll a sum of 3 or 8, you win ₱600. If you roll a sum of 10, you win ₱400. However, you lose ₱500 for anything else. If you continue to play the game, how much do you expect to win or lose in the game?

Find the corresponding area between z=0 and each of the following

1.z=0.85

2.z=1.27

3.z=2.86

4.z=1.05

5.z=-2.96

Determine if the following situations use as random or non-random sampling. Also, write 

              the type of random or non-random sampling technique used.

1. Selection of students name 10 written in rolled papers in a box containing

      100 names.__________________

2. The respondents are selected according to class size whereas 30 for freshmen, 20 for 

       Sophomores, 10 for juniors, and 5 for seniors. ____________________

3. The minority groups of senators are to be interviewed._______________________

4. Five hundred “likes” from netizens in facebook is used as a basis for making decisions._______________________

5. Two thousand respondents nationwide are chosen for national election purposes from 

      populations of regions down to barangays.____________________

p,p+7,p+14,.... is arithmetic sequence

Find n term and Find the smallest value of p for which 2021 is a term in the sequence.

P ( 0 < z < 2.0 )

The average time for a courier to travel from Tagum to Davao is 120 minutes, and the standard deviation is 15 minutes. If there are 1255 courier, how many takes between 100 to 140 minutes to travel from Tagum to Davao?

A meeting of consuls was attended by 4 Americans and 2 Germans. If three consuls were selected at random one after the other, list down all possible outcomes for the random variable G (number of Germans)