Homework 3

• Binomial coefficients and binomial theorem, probability
  • Write the binomial expansion of (x-2)¹⁰. (You do not have to simplify/compute the coefficients.)
  • Use the first few terms of the binomial expansion of (1+0.002)¹⁰⁰ to estimate the value of 1.002¹⁰⁰ correct to two decimal places.
    Hint: start with just one term and try using more and more terms. As soon as the answers for k terms and for k+1 terms agree to three decimal places, you have the desired approximation.
  • There were 15 dimes, 20 nickels, and 25 pennies in a cup. Five coins were selected at random. None of them are nickels. What is the probability that exactly three of them are pennies?
• Rates, proportional reasoning
  • (MH 9-10, 2009) 5 cows can eat 2 acres of grass in 10 days. How many days will it take 10 cows to eat 6 acres of grass?

  ---

  This page was last revised on 4 February 2011.