Question

Hi, I am doing up my homework on mathematics and here are some questions. I want to cross-reference my answers thank you. Decide if the statements below are True or False. Please include some rough workings for me to understand:

(1) Mr. Tan borrowed $500,000 from Bank XYZ at 5% annual interest to be repaid monthly over 20 years. The amount that he pays back to XYZ each month is between $3000 to $3500.

(2) Continuing from (1): after 15 years, Mr. Tan still owing the bank between $120,000 to $160,000.

(3) 8 persons can sit at a round table with 10 seats 9!/2 ways.

(4) 8 persons sit at a round table with 10 seats so that there is exactly one person between the two empty seats in 8! ways.

(5) On a square grid, you are allowed to go only east (i.e., horizontally to the right) or north (i.e., vertically upwards), moving 1 step at a time. The number of ways (i.e., the number of such paths) by which you can go from (3,3) to (5,5) is8 3.

(6) The number of ways in which 10 identical red balls and 7 identical blue balls can be arranged in a line is17 7.

(7) The sumP2019 k=0 2k is an even number.

(8) According to Benfords law, the probability of 5 being the leading digit of a long list of positive integers (such as the population of various cities) is 0.0969 (to 4 decimal places).

(9) Three fair dice are thrown. The expected value of the total score obtained is 10.5

(10) If the expected number of heads in 5 independent tosses of a coin is 3, then the coin must be fair.

Answer 1