MATH500 Week 1 DiscussionNumber Forms, Signed Numbers, & Exponents (graded)Being able to convert from fractions to decimals to percents, and back, is an important ability since different situations require different formats. In this discussion, we will practice converting back and forth. Weâll also work with fractions, including a review on how to multiply, add, and convert from different forms.1) Convert 4.0005% into a decimal.2) Convert 400.05% into an improper and a mixed fraction.3) Convert 4.0555 into an improper and a mixed fraction.4) Evaluate 3/5 x 20/25 and simplify.5) Evaluate 2 3/4 + 1 1/2 and simplify.Using signed numbers in basic arithmetic is an important skill to have since many applications use a variety of numbers. In this discussion, we will practice several arithmetic operations, including the use of exponents.6) Multiply the following numbers:a) (+2)(+2) = b) (+2)(-2) =c) (-2)(-2) =7) Divide the following numbers: a) +2/+2 =b) +2/-2 =c) -2/-2 =8) Add the following numbers: a) (-10) + (-20) =b) (+10) + (-20) =9) Subtract the following numbers: a) (-20) â (-30) =b) (-20) â (+30) =c) (+20) â (-30) =10) Evaluate the following exponentials: a) (-1)^3 =b) â1^3 =c) (-1)^2 =d) â1^2 =MATH500 Week 2 DiscussionAlgebraic Operations and Applications (graded)When solving the following questions, show each step of the solution along with the final results. If there is no work to show, be sure to fully explain your solution method.1. Simplify the following algebraic operations:a) 7x â 2(x-2) + 5(x+3)b) (x+2)(x-4) + 3x + 12. Suppose a student has earned the following grades on her first four quizzes: 83, 72, 89, 78. What must she score on her fifth quiz in order to have a mean of 80 on all of her quizzes?3. The perimeter of a rectangle is twice the length plus twice the width. The area of a rectangle is the product of its length and width. Suppose we let l represent the length and w represent the width of a rectangle.a) Write an algebraic expression that represents the perimeter.b) Write an algebraic expression that represents the area.c) Calculate the perimeter of a rectangle 12 inches long and 20 inches wide. d) Calculate the area of the rectangle described in Part C.MATH500 Week 3 DiscussionSolving Equations and Applications (graded)1. Solve each of the following equations for the unknown variable.a) 15x + 40 = 8x – 9 b) 7y – 1 = 23 – 5yc) 9(2x + 8) = 20 – (x + 5)d) 4(3y – 1) – 6 = 5(y + 2)2. Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9600. How much did he pay for each piece of land?3. A major car rental firm charges $57 a day with unlimited mileage. A discount firm offers a similar car for $24 a day plus 22 cents per mile. How far must you drive in a day in order for the cost to be the same at both firms?MATH500 Week 4 DiscussionLinear Equations and Applications (graded)Linear Equations and Applications:Find the x- and y-intercepts for the line given by the equation 3x + 2y = 12Find the equation of the line that passes through the points (3,1) and (2,-1). Write the equation in slope-intercept form.Find the equation of the line that passes through the points (1,1) and (-2,10). Write the equation in slope-intercept form.Suppose a business purchases a new tractor at an original cost of $42,000. Further, suppose this tractor has a useful life of 8 years and a salvage value of $10,000.a) Use the Straight-Line Method to find the yearly depreciation on this tractor.b) How much is this tractor worth after 3 years?c) Find a formula that calculates the tractorâs worth after t years. What is the maximum allowable value for t?MATH500 Week 5 DiscussionSystems of Equations and Applications (graded)1. Solve the following system of equations.3x + 4y = 42x + y = 62. Solve the following system of equations.2x – 3y = 135x + 2y = 43. The Kraft Co. manufactures computer chips at a variable cost of $4 per chip and sells them for $10 each. If the fixed cost is $12,000 per month, what is the number of chips they would need to produce at the break-even point?4. The Sunshine Bakery sells pies at a fixed price of p dollars per pie. The total number of pies demanded daily, D, is related to the price, p, in dollars by the equation:D = -10p + 200On the other hand, the daily supply of pies, S, is related to the price, p, per pie by the equation:S = 15p – 50Determine the equilibrium price of pies; that is, the price at which the supply, S, and demand, D, are equal.MATH500 Week 6 DiscussionInterest (graded)You invest $5,800 over a period of 30 months at 5 1/4% simple interest. What is the total value of your investment at the end of the 30 month period?Mary deposits $15,000 into a savings account that pays 3.75% interest compounded daily. What will the balance be after five years?Suppose Mary needs $32,000 in five years for a new car. If her account pays 3.75% interest compounded daily, how much must she deposit today to have the money for the car? What is the term used for this value?The Happy Savings Bank offers a nominal interest rate of 6% compounded quarterly, whereas the People’s Credit Union offers a nominal interest rate of 6.2% compounded semi annually. Suppose you want to open a new bank account and you have narrowed your choices to one of these institutions.What is the Effective Interest Rate for Happy Savings Bank?What is the Effective Interest Rate for People’s Credit Union?Where should you open your account?MATH500 Week 7 DiscussionAnnuities and Loan Payments (graded)Use the Annuity Calculator as appropriate to help answer the following questions. Be sure to work through the examples in the lecture first. You can access the Annuity Calculator from either the lecture, or with this link: .net/re/LaunchDotNextOutboundSSO.asp?ssoType=PearsonMML&target=GENERICMXL_LINK%3Fhttp%3A//media.pearsoncmg.com/pcp/pls/mycourse/custom/math_custom/schools/annuity_calculator/index.html”>Annuity CalculatorSuppose Mary deposits $200 at the end of each month for 30 years into an account that pays 5% interest compounded monthly.How much total money will she have in the account at the end?How much total money did Mary actually deposit?How much total interest did the account earn over that period?Suppose instead of making monthly deposits, Mary decides to deposit a âlump sumâ into the account. How much must she deposit? What is this value also called?Suppose a retiree wants to buy an ordinary annuity that pays her $2,000 per month for 20 years. If the annuity earns interest at 3.5% interest compounded monthly, what is the present value of this annuity?Suppose a student wants to be a millionaire in 40 years. If she has an account that pays 8% interest compounded monthly, how much must she deposit each month in order to achieve her goal of having $1,000,000? What is the present value of this annuity?Suppose John sells his house and earns a profit of $600,000. With the profit, he buys a 20 year annuity that earns 6.5% interest compounded monthly. What monthly payment will John get?You wish to purchase a house for $200,000 with 20% down. You will have it financed over 30 years at a rate of 8%. In addition, your yearly real estate tax is $4,800 while your monthly insurance payment on the home will be $30. What is your monthly mortgage payment? How much does your house cost per month including principal, interest, real estate taxes, and insurance?
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