Math Answers

1. In a viral pole test it is known that in a group of five (5) people, exactly one (1) well test positive. If they are tested one by one in random under for confirmation, what is the probability that only two (2) tests are needed?

2. A basket of fruits contains eight (8) apples and ten (10) oranges. Half of the apples and half of the oranges are rotten. If one (1) fruit is chosen at random, what is the probability that a rotten apple or an orange is chosen?

3. A small-time bingo card cost P100.00 for 5 games. The prize for the first three games is P5,000.00, the fourth is P10,000.00 and the last prize is P20,000.00. if 1,000 bingo cards are going to be sold and you could only win once, what is the expected value of a ticket?

7. You pick a card from a deck. If it is a face card, you will win P500.00. if you get an ace, you will win P1,000. If the card you picked is red you get to P100.00. for any other card, you will win nothing. Find the expected value that you can possibly win.

1. The number of typing errors on page follows a poisson distribution with a mean of 6.3. find the probability of having exactly six (6) errors on a page.

2. One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?

3. If one ball is drawn from 3 boxes, the first containing 3 red, 2 yellow, and 1 blue, the second box contains 2 red,2 yellow, and 2 blue, and the third box with 1 red, 4 yellow, and 3 blue. What is the probability that all 3 balls drawn are different colors?

Find the center of mass of the region bounded by y=(x-2)^2 and y=4.

Consider the decomposition of

(6x^3+x−3)/(x^2−2x+1)

Use Descartes' Rule of Signs to find the possible number of negative zeros of p(x)=2x5+x4+x3−4x2−x−6

Calculate the Laplace transform of

• (t) integral from (0 to t) (T)e^(T)dT

Find the general solution for the differential equation

-y"=6x + xe^x

(a) using method of undetermined coefficients

(b) using variation of parameters

Solve the following system of equations and provide a graphical representation of the solution.

y - x = 1

x² + y² = 13

15. I provide 5 chairs, one for each person that is going to wait in the line. In how many different ways can they stand in line? 

DIRECTIONS: Determine the critical value and illustrate the rejection region under the

normal curve by using the given information.

4

Ha α Critical Value Illustration

1. p ≠ 0. 52 0.01

2. p > 0.35 0.10

3. p < 0.7. 0 0.05

4. p > 0.65 0.05

5. p ≠ 0. 46 0.01