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Complex Numbers

Find the real and imaginary parts of the complex number 4 minus 3i divided by 2 plus i.

Principle of Mathematical Induction

Prove by mathematical induction that the sum of the first n natural numbers is equal to n times (n plus 1) divided by 2.

Trigonometric Identities

• Prove that tan theta plus cot theta is equal to sec theta times cosec theta.

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Sets

Let A be the set of all prime numbers less than 10, and B be the set of all odd natural numbers less than 10. Find A union B and A intersection B.

Probability

A card is drawn at random from a standard deck of 52 cards. What is the probability of drawing a queen or a heart?

Sequences and Series

For an arithmetic sequence with first term 5 and common difference 3, find the 10th term.

Quadratic Equations

Solve the equation x squared minus 5x plus 6 equals 0 and find the roots

Permutation and Combination

In how many ways can 5 people be seated in a row of 7 chairs?

Statistics

A data set consists of 15, 20, 35, 40, 50, 50, and 55. Find the median and mode of this data set.

Environmental Chemistry

1. What is acid rain? Explain its causes and effects on the environment.