Math Answers

In each of the 4 races, the democrats have 60% chance of winning.

Assuming that the races are independent of each other, what is the

probability that:

a) The Democrats will win 0 races, 1 race, 2 races, 3 races, or 4

races?

b) The Democrats will win at least 1 race.

c) The Democrats will win a majority of the races.

In each of the 4 races, the democrats have 60% chance of winning.

Assuming that the races are independent of each other, what is the

probability that:

The Democrats will win a majority of the races.

Let f : A → B be a function.

1. Show that for the identity function iA on A we have f ◦ iA = f.

2. Show that for the identity function iB on B we have iB ◦ f = f.

Show that the curve with parametric equations

x = sin t and y = sin(t + sin t) for 0 ≤ t ≤ 2π

List the quadruples in the relation { a,b,c,d} where a, b, c, d are integers with

0 < a < b < c < d < 8

The area A of a circle is increasing at a constant rate of 2cm2s−1. If the area of the circle is given by A = πr2, what is the rate of change of the radius when the radius is 4cm?

The area A of a circle is increasing at a constant rate of 2cm2s−1. If the area of the circle is given by A = πr2, what is the rate of change of the radius when the radius is 4cm?

1. Consider the function y = x2 + 3x + 5. 2x−3

(a) Determine the domain of the function.

(b) Determine the range of the function.

(c) Determine the intercepts of the function.

(d) Find the asymptotes if they exist.

(e) Find the turning points (if they exist) and determine the type of turning points they are.

(f) Manually sketch the graph of the function.

Read the question and solve the problem below. Write your complete solution.

Mike Marquez purchased a lawn tractor for Php 9,000. He made a down

payment of Php 1,000 and financed the rest at 7% payable in 24 months. He paid off

the loan at the end of the fifteenth months. Find the amount of his refund using the rule

of 78s.

1. Consider the function y = x2 + 3x + 5. 2x−3

(a) Determine the domain of the function.

(b) Determine the range of the function.

(c) Determine the intercepts of the function.

(d) Find the asymptotes if they exist.

(e) Find the turning points (if they exist) and determine the type of turning points they are.

(f) Manually sketch the graph of the function.