Math Answers

Suppose 5 points are chosen at random in the interior of an equilateral triangle

T where each side has length two inches. Show that the distance between two of

the points must be less than one inch.

Consider a tournament with n players where each player plays against every

other player. Suppose each player wins at least once. Show that at least 2 of the

players have the same number of wins.

Find the minimum number n of integers to be selected from S = {1, 2, . . . , 9} so 

that: (a) The sum of two of the n integers is even. (b) The difference of two of the 

n integers is 5.

In the Philippines, the COVID-19 cases drops from 386,000 in March, 2020 to 230,000 in July, 2020. If the cases is following an exponential pattern of decline, what is the expected cases in December, 2020?,

1. Solve the following Bernoulli's Differential Equations. Show your solutions.

a. dy/dx + (1/3) y = e^x y²

b. x (dy/dx) + y = xy³

c. dy/dx + (2/x) y = -x² cos x y²

d. x²y-x³ (dy/dx) = y² cos x

Valentina’s Pizzas Corporation is considering the purchase of a new restaurant for $8 million. The forecasted net cash flows (net of the costs associated with running the restaurant) are $3 million a year for the next 15 years. A major refurbishment costing $2 million will be required after both the fifth and tenth years. After 15 years, the restaurant will be closed and the restaurant’s venue is expected to be sold for $16 million. If the discount rate is 8%, what is this investment’s NPV?

1. Define the difference between a well-defined relationship and a poorly-defined relationship and draw graphs to depict the differences. 2. What are the unique characteristics of interpretation in logistic regression? 3. Explain the concept of odds and why it is used in predicting probability in a logistic regression procedure 

An engineering company wants to make a loan. The bank constructs a credit check through accessing historic data of companies. The data carried company ID, Years in operation, Size of the company (big or small), loan amount, times a company was overdue and whether or not the company defaulted.

Company_ID Years Size Loan Amount Times overdue Default

1 5 B R60000 1 NO

2 9 B R90000 12 YES

3 3 S R40000 7 YES

4 15 B R20000 15 YES

5 4 S R10000 0 NO

i. Which variable is the dependent variable?

ii. Categorize the variables numerically for analysis purposes.

iii. What are the assumptions of Logistic regression?

translate the given situations of linear inequality into mathematical statements.

The value of one Philippine peso (p) is less than the value of one US dollar (d). ______________________

According to PSA, there are more female (f) Filipinos than male (m) Filipinos. ______________________

To get a passing mark in school, a student must have a grade (g) at least 75. ______________________

The expenses of food (f) is greater than the expenses for clothing (c). ______________________

Seven times the number of male teachers (m) is the number of female teachers (f). __________________

Becheil bought two blouses and a pair of pants. The total amount she paid for the items is not more than P980. What is the correct mathematical statement that illustrates the given situation?

2x+ y ≥ P980 b. 2x+ y ≤ P980 c. 2x+ y < P980 d. 2x+ y > P980