Math Answers

Suppose you are buying face mask for yourself, your friends, and family during this covid-19

pandemic. The face mask shop has a deal going, if you buy one facemask for 35 pesos, then

additional face masks are only 30 pesos each. Using a short bond paper, do the following:

a. Represent this situation into a rational equation showing the price per face mask based

on the number of face masks.

b. Determine the horizontal asymptote and explain what the horizontal asymptote

represents.

c. Graph the function appropriately and determine its domain and range.

d. Is the original function one-to-one? Explain

Compare and contrast Descriptive and Inferential Statistics both in concept and in applicability.

1. Allie is conducting a research on personality traits and substance use among Filipino young adults. For his sample, he chose 50 of his friends to be his respondents. Did he commit an error in choosing his sample? Why or why not?

2. Remy wants to know more about the life satisfaction and academic performance of SLU students. For his sample, he chose 100 students from each school to be his respondents. Did he commit an error in choosing his sample? Why or why not?

The data represents the quiz scores of psychology majors in one of their major subjects.

Mean = 22.5 SD = 5.50 N = 60

1. Find out the number of students with scores equal to and above 30.
2. How many students have scores equal to and below 30? 
3. Find out the range of scores of the middle 10 students.

Examine the convergence of the series

a) 3×4/5^2+5×6/7^2+7×8/9^2+.........

b) 1+4x+4^2x^2+4^3x^3+......(x>0)

Let f:[-3,3 ]->R defined by f(x)=5(x)+x^3,where [x]denotes the greatest integer < =x.show that this function is integrable

The probability of winning in a lottery is 1/100. You buy a ticket for 50 different lotteries. ◦ What is the probability that you win exactly in one of these 50 lotteries? ◦ What is the probability that you win at least one of these 50 lotteries?

(D ^ 2 + 3D + 2) * y = sin 2x + 5 degrees + log 3

4. Let P(n) be the statement that 1+2+...+n'3D (n(n + 1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f) Explain why these steps show that this formula is true whenever n is a positive integer. 5. Prove that 12+32+52+ + (2n + 1)² = (n + 1)

4. Let P(n) be the statement that 1+2+...+n'3D (n(n + 1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f) Explain why these steps show that this formula is true whenever n is a positive integer. 5. Prove that 12+32+52+ + (2n + 1)² = (n + 1)

Given that y'=x+y with y(0) = 1 find y(0.1).h=0.05 by Euler's modified method.