Exercises in Statistics: Finding Equilibrium Quantity and
Equilibrium Price
1. The difference between two numbers is twelve. Three times
the smaller number is four less than twice the larger number. Find the smaller
number.
2. John has $20,000 to invest. As his financial consultant,
you recommend that he invest in Treasury Bills that yield 5%, Treasury bonds
that yield 7%, and corporate bonds that yield 9%. John wants to have an annual
income of $1,280, and the amount invested in Treasure Bills must be two times
the amount invested in corporate bonds. Find the amount of each investment.
(Hint: This is the system of three equations and three variables)
3. A tree removal service assesses a $400 fee and then
charges $80 per hour for the time on an owner’s property. Hint: This is a
linear function.
a) Is $750 enough for 5 hours work?
b) Give the domain and range
If:
f (x) = { (x+1@-x^2@?3x)?
if x < -2
if -2 ? x ? 1
if x > 1
Find
f(-5)
f (1/2)
f (2.784)
5. Florida Powers & Light Company supplies electricity
to residential customers for a fixed monthly customer charge of $5.25 plus
6.787 cents per kilowatt-hour.
a) Write an equation that relates the monthly charge C, in
dollars, to the number x of kilowatt-hours used in a month.
b) What is the monthly charge for using 200 kilowatt-hours?
1. A newly issued affirmative action released by industrial
organizations has led to an increase in the number of minors in managerial
positions. Baan Pu has vacancies for three managers that it will fill from
among five minors and eight majors.
What is the probability that no major is selected?
What is the probability that at least one minor is selected?
What is the probability that exactly one minor is selected?
2. Find the derivatives (dy/dx) of the following functions.
Please show the steps you take to solve each one.
f (x)= (2x+5)/5x
f (x)= (?5x?^2- 3x )2
y3 = x + 1
3. This question requires the creation of a graph in a word
document and submitted via the link below.
Let the supply and demand functions for Toyota Altis be
given by: S(q) = (3/2)q+1000 and D(q) = 25000 – (3/2)q , where q is the number
of cars.
Graph these functions on the same axes. Also, find the
equilibrium quantity and the equilibrium price.
4. Find the slope of the tangent line using the definition
of the derivative to the function given below. Then find the points on the
function where the tangent line is horizontal.
f (X)= (4/(3)) x^3 – 9x
5. Determine the equation of the line through (2, 5) and
perpendicular to y = -2.
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