Math Answers

 Suppose that a vector a in the xy-plane points in a direction that is 47◦ counterclockwise from the positive x-axis, and a vector b in that plane points in a direction that is 43◦ clockwise from the positive x-axis. What can you say about the value of a · b?

Given R is a relation from A = {1,2,3,4,5}, R={(1,1),(2,2),(2,3),(2,4),(3,3),(4,4),(4,5)}.

Is R an equivalence relation?

A circle is placed in a square with a side length of 12 cm, as shown below. Find the area of the shaded region. use the value 3.14 for r, and do not round your answer. Be sure to include the correct unit in your answer.

Calculate the total number of words that can be formed using the

letters of the word “MISSIPPI” if two ‘S’ and two ‘I’ are adjacent to

each other.

A frog jumps and takes 2 seconds to land. The path of the frog’s flight is best modeled by the graph of f(x) = -x² + 2x. What is the maximum height of the jump?

A population of 25 year- old female has a mean salary of P20,800 with a standard deviation of P1200. If a random sample of 10 is considered from the population, what is the probability that their salary is greater than P20900?

Can two or more three-dimensional solid figures have the same volume? Why or why not?

Construct a truth table for each of these compound propositions

(p ⊕ q) → (¬q ↔ r)

How many different strings can be made from the letters in the word rat?

A boy lives at X and wants to go to school at Z. From his home to X he has to first reach Y

and then Y to Z. He may go X to Y by either 3 bus routes or 2 train routes. From there, he can

either choose 4 bus routes or 5 train routes to reach Z. How many ways are there to go from X to

Z?