Scientific Notation Problems

Section 3: Scientific Notation 1. How many one hundred dollar bills would you need to have ten thousand dollars? Explain. 2. How many 1,000 are there in 10 billion? Explain. 3. Explain in your own words: a. How to convert a standard number to scientific notation. b. How to convert a numb...

Examples using Scientific Notation, Proportions, and Per Capita

Per Capita 1) The National Oceanic and Atmospheric Administration (NOAA) reported that there are 17.8 million feet of Atlantic coastline in the state of North Carolina. If the population of North Caroline is approximately 9.5 million, find the number of feet of coastline per capita in North Carol...

Merry-go-round: cyclic equation to model the distance

Brenna's mom, Mrs. Herstone, is watching Brenna playing at the park. Some children are pushing Brenna around the merry-go-round. Mrs. Herstone decides to take some data, so she started her stopwatch. At 3.5 seconds Brenna is farthest from Mrs. Herstone 26 feet away. When the stopwatch reads 4.2...

Emile's Inheritance

Emile got a letter in the mail saying that a wealthy relative had left him an inheritance. At a meeting the next week, a lawyer read the following statement. To Emile, because he likes math problems, I leave a choice. He can have one of two inheritances. He must make his choice before leavin...

Simple volume of a cylinder with unit conversion.

Since this module focuses on measurement it will be very important that mathematical conversions be clearly demonstrated throughout your problem write-up. For example, if you are converting 28 yards to meters, you must track your calculations with cancellation of units as seen below: 28 yards t...

Parking Option Best for the Employee on a Monthly Basis

A downtown employee is looking for the best option for parking a car during a 5 day work week. One parking garage offers unlimited parking at a flat rate per month. Another garage offers an hourly rate for parking. Which option is best for the employee on a monthly basis? Consider that the employ...

Proving a Time Series is White Noise and Stationary

Suppose {e_t} and {E_t} are two independent white noise processes with variance sigma^2 and sigma^2_e respectively. (a) Show that {v_t = e_tE_(t-1)} is also a white noise and calculate its variance. (b) Show that y_t = v_t - 0.5_(vt-1) + 3e_(t-1) is stationary.

Problems of Polynomials

1. Write a function whose graph is the graph of y = (x+2)^2, but is refelcted about the x-axis. 2. Determine whether the given function is linear or nonlinear? If the function is linear, determine the slope. x y = f(x) 1 -12 2 -7 3 -5 4 -4 5 -5 3. Form ...

Finding the Equation of the Exponential Functions

Find an equation of the exponential function y=g(x) , whose graph passes through the 2 given points. a) (0,5) (3,9) b) (2,24) (4,8) Please show how you got the answer. And find a equation of the linear function y=f(x) for the same points.

Find the x-intercept or a y-intercept for given function

Please help answer the following questions: 1. Find all intercepts of the function f(x)=4x^3-7x^2-16x+28 . For each intercept, show your algebra, then state the intercept using correct function notation and as an ordered pair. Clearly state whether the intercept is an x-intercept or a y-intercep...

Vector Calculus and Linear Algebra

Question 4 Find the work done by the force F (x,y,z) = -x^2y^3 i + 4j + xk on moving charged electric particle along the path given by the equation r (t) = 2cos t i + 2sintj + 4k, where the parameter t varies from pi/4 to 7pi/4. Question 5 Displacement of the spring system with friction ...

Applied Algebra: Minting Pennies

6. Owing to the rising cost of copper, in 1982, the US Mint changed the composition of pennies from 95% Copper + 5% Zinc to 2.5% Copper + 97.5% Zinc to save money in minting pennies. Your favourite aunt has a collection of 5,000 pennies minted prior to 1982 and she intends on gifting the collection ...

Variance on Shelter Sample Data

You want to make a statement about the variability in the costs of personnel shelters. After collecting sample data (cost in $K) on 9 shelters you perform some preliminary calculations. Given the information provided: The coefficient of variation is about 17.64% The variance is a...

Solve the Rational Equation

Please help solve this rational equation and please explain what a rational equation is. 1/b-5 - 10/b^2-5b+25 = 1/b+5

Non-dimensionalising Differential Equations

Two species with populations N1(t) and N2(t) interact according to the model: (dN_1/d_t)=r_1N_1(1-(N_1/K_1) - b_12(N_2/K_1), (dN_2/d_t)=r_2N_2(1-b_21(N_1/K_2), Non-dimensionalise the system (7) so that: (d_u/d_t) = u (1- u - au), (d_u/d_t) = pv (1-Bu), finding explicit formulae for t...

Algebra: Elimination and Substitution Methods

1. Solve the following system of equations using the Substitution method: 5X-7Y= - 18 4X+3Y= 20 2. Solve the following system of equations using the elimination method: 2X-3Y=12 -2X+3Y=12 Solution: Computation of the Equations 2X-3Y =12 -2X+3Y =12 3. A total of $80,000 is invested in ...

Graph rational equation

A. Graph the function  =  f(x) = x-2/x^2 - 3x + 2 B. Find the domain and range of , showing all work. C. Find the → , showing all work, or explain why the limit does not exist. D. Find the → , showing all work, or explain why the limit does not exist. E. Apply th...

Solving an example linear programming question

1. A component has a reliability of 0.75. How many identical components do we have to add n parallel to the frst to increase the overall reliability to 0.95? You may use the following general formulas R_sys = 1-(1-R1)(1-R2)...(1-Ri)...(1-Rn) Ri=e^-(lamda*t) 2. Find both the minimum and maximu...

Submodules of polynomial ring K[x]

Which of the following sets of polynomials n K[x], K commutative are K-modules:(a) all polynomials of degree exactly ; (b) all polynomials of degree at most 4; (c) all monic polynomials; (d) all polynomials of even degree?

Bank reconciliations and horizontal models for interest

Prepare a bank reconciliation as of August 31 from the following information: a. The August 31 balance shown on the bank statement is $9,810. b. There is a deposit in transit of $1,260 at August 31. c. Outstanding checks at August 31 totaled $1,890. d. Interest credited to the account during Aug...

Algebra Calculations

Can you please explain how to do these problems? 1. Evaluate 3x-4y/ 2z when x= -2, y=3, z=4 . Express your answer as a fraction. 2. Use the order of operations to simplify the following expression. (-2)2 -3 2 3. Write the statement as an algebraic equation: 'The difference between x and 2...

Several Statistics Example Questions

6. Why can't you obtain a correlation coefficient greater than ±1? 8. As the value of r approaches ±1, what does it indicate about the following: a) The consistency in the X-Y pairs b) The variability of the Y scores at each X c) The closeness of the Y scores to the regression line d) the a...

Accounting: Liabilities and Shareholders' Equity

Liabilities and Shareholders' Equity Accounts payable............................................... $5,520 $4,970 Accrued expenses............................................... 8,572 4,310 Non-current liabilities......................................... 4,450 1,535 Common...

Calculating new table factors for investments

To determine the compound amount of an investment of $10,000 with an interest rate of 6% compounded monthly after 4 years requires you to use a table factor that goes beyond the Compound Interest Table. Calculate the new table factor for this investment. (Points : 2.5) 5. Now, us...

Computing Four Profitability Ratios of Companies

I need to calculate the four profitability ratios that can be computed from the information on the Conner Company. The data is presented below: Average total assets 1,700,000 Net income 250,000 Net sales 1,400,000 Average common stockholders' equity 1,000,000 Net cash provid...