1. The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r to the nearest tenth of a percent. P=2000.00 A=2042.50 t=3 months 2. A radio commercial for a loan company states: \"You only pay 33 cents a day for each $500 borrowed.\" If you borrow $2,381 for 224 days, what amount will you repay, and what annual interest rate is the company actually charging? (assume a 360 day year.) a. Amount you repay= $_______________ (round to two decimal places) b. Annual interest rate=% _____________ (round to four decimal places) 3. Given the annual interest rate and the compounding period, find I, the interest rate per compounding period. 5% compounded monthly I=_____% per month (type an integer or decimal rounded to the nearest thousandth as needed) 4. 3.9% compounded quarterly I=_____% (type an integer or decimal rounded to the nearest thousandth as needed) 5. An investment company pays 4% compounded semiannually. You want to have 18,000 in the future. (A) How much should you deposit now to have that amount 5 years from now? $____ (round to the nearest cent) (B) How much should you deposit now to have that amount 10 years from now? $____ (round to the nearest cent) 6. What is the APY for money invested at each rate? (A) 5% compounded monthly (B) 6% compounded monthly (A) APY=___% (Round to three decimal places as needed) (B) APY=___% (Round to three decimal places as needed) 7. How long will it take $4,000 to grow to $21,000 if it is invested at 4% compounded monthly? ___ years (round to the nearest tenth of a year) 8. Use the future value formula to find the indicated value. FV=$5765; n=9; i=0.05;PMT=? PMT=$___ (round to the nearest cent) 9. Acme annuities recently offered an annuity that pays 5.4% compounded monthly. What equal monthly deposit should be made into this annuity in order to have $74,000 in 17 years? The amount of each deposit should be $____ (round to the nearest cent) 10. E-loan, an online lending service, recently offered 36 month auto loans at 4.5% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $501, how much can you borrow from Eloan? What is the total interest you will pay for this loan? You can borrow $____ (round to two decimal places) You will pay a total of $____ in interest. (round to two decimal places) MATH 106 QUIZ 4 NAME: _____ _________________ Professor: Dr. Katiraie INSTRUCTIONS The quiz is worth 100 points. There are 10 problems (each worth 10 points). This quiz is open book and open notes, unlimited time. This means that you may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our course schedule of the syllabus. You must show your work to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. Be sure to include your name in the document. Consult the Additional Information portion of the online Syllabus for options regarding the submission of your quiz. If you have any questions, please contact me by email (farajollah.katiraie@faculty.umuc.edu ). MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the maximum value of the function, if it exists, on the given feasible region. Find the maximum of z = 4x + 8y A) 102 B) 120 C) 76 D) 112 E) none of the above 1) _______ the minimum value of the function, if it exists, on the given feasible region. Find the minimum of z = x - 2y 2) _______ 2) Find A) -1 B) -13 C) -28 D) -16 E) None of the above 3) Use graphical methods to solve the linear programming problem. Maximize Subject to: z = 6x + 7y 2x + 3y 12 2x + y 8 x 0 y 0 A) Maximum of 32 when x = 3 and y = 2 B) Maximum of 32 when x = 2 and y = 3 C) Maximum of 24 when x = 4 and y = 0 D) Maximum of 52 when x = 4 and y = 4 E) None of the above 3) _________ z =6 x +7 y 2 x +3 y 12 2 x +y 8 x 0 y 0 That is: 2 x +3 y =12 2 x +y =8 x =0 y =0 solve; 2 x +3 y =12 2 x +y =8 x =3, y =2 if ( 3, 2 ) , z =6 x +7 y z =32 4) A college student can spend no more than 8 hours a week tutoring. She charges $10 an hour to tutor finite math and $13 to tutor algebra. She limits herself to no more than 3 hours per week to tutor algebra and spends at least 1 hour a week tutoring each subject. How many hours per week should she spend tutoring each subject to maximize her income? What is her maximum weekly income? 4) _________ Hint: Let x = number of hours per week to tutor finite math and y = number of hours per week to tutor algebra Then use graphical methods to solve the following linear programming problem: Maximize z = 10x + 13y Subject to: x + y 8 y 3 x 1 y 1 A) 4 hours of finite math and 4 hours of algebra; maximum income is $92 per week B) 7 hours of finite math and 1 hour of algebra; maximum income is $83 per week C) 5 hours of finite math and 3 hours of algebra; maximum income is $89 per week D) 3 hours of finite math and 5 hours of algebra; maximum income is $95 per week E) None of the above z =10 x +13 y x +y 8 y 3 x 1 y1 That is; z =10 x +13 y x +y =8 y =3 x =1 y =1 If y =3 then x +3 =8 x =5 ( 5,3) If x =1 then 1 + y =8 y =7 ( 1, 7 ) If y =1then x +1 =8 x =7 ( 7,1) At ( 5,3) , z =10 x +13 y z =89 At ( 1, 7 ) , z =10 x +13 y z =101 At ( 7,1) , z =10 x +13 y z =83 Max z =101 At ( 1, 7 ) 5) Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, C = {v, w, x, y, z}. Find the elements in the set A B' 5) _______ A) {t, v, x} B) {u, w} C) {r, s, t, u, v, w, x, z} D) {q, s, t, u, v, w, x, y} and E) None of the above U = { q, r, s, t, u, v, w, x, y, z} , B =U - B ={ q, r , s, t, u, v, w, x, y, z} - B = { q, s, y, z} ={ r, t, u, v, w, x} A B ={ q, s, u, w, y} { r, t, u, v, w, x} ={ u, w} 6) Use the counting formula to solve the following problem. If n(B) = 12, n(A B) = 3, and n(A B) = 21, find n(A). 6) _______ A) 12 B) 14 C) 9 D) 10 E) None of the above n ( A B ) =n ( A ) +n ( B ) - n ( A B ) 3 =n ( A ) +12 - 21 3 =n ( A ) - 9 n ( A ) =12 7) If n(A) = 32, n(B) = 93 and n(A B) = 109, what is n(A B)? A) 8 B) 18 C) 48 D) 16 7) _______ E) None of the above n ( A B ) =n ( A ) +n ( B ) - n ( A B ) =32 +93 - 109 =125 - 109 =16 Solve the following problems. 8) At East Zone University (EZU) there are 897 students taking College Algebra or Calculus. 520 are taking College Algebra, 450 are taking Calculus, and 73 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? 8) _______ A) 824 B) 374 C) 377 D) 447 E) None of the above n ( A ) =520 n ( C ) =450 n ( A C ) =897 n ( A C ) =73 n ( eople taking Calculus but not algebra ) =450 - 73 =377 9) A restaurant offered salads with 8 types of dressings and 4 different toppings. How many different types of salads could be offered? 9) _______ A) 32 types B) 16 types C) 12 types D) 64 types E) None of the above 8 4 =32 10) How many ways can a committee of 5 be selected from a club with 10 members? 10) ______ A) 30,240 B) 252 C) 50 D) 100,000 E) None of the above n! ( n - r ) ! r ! = 10! ( 10 - 5 ) ! 5! 10! 5! 5! 6 7 8 9 10 = 5! 6 7 8 9 10 = 1 2 3 4 5 6 7 8 9 = 3 4 =2 7 2 9 =252 = MATH 106 QUIZ 4 NAME: _____ _________________ Professor: Dr. Katiraie INSTRUCTIONS The quiz is worth 100 points. There are 10 problems (each worth 10 points). This quiz is open book and open notes, unlimited time. This means that you may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our course schedule of the syllabus. You must show your work to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. Be sure to include your name in the document. Consult the Additional Information portion of the online Syllabus for options regarding the submission of your quiz. If you have any questions, please contact me by email (farajollah.katiraie@faculty.umuc.edu ). MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the maximum value of the function, if it exists, on the given feasible region. Find the maximum of z = 4x + 8y A) 102 B) 120 C) 76 D) 112 E) none of the above 1) _______ the minimum value of the function, if it exists, on the given feasible region. Find the minimum of z = x - 2y 2) _______ 2) Find A) -1 B) -13 C) -28 D) -16 E) None of the above 3) Use graphical methods to solve the linear programming problem. Maximize Subject to: z = 6x + 7y 2x + 3y 12 2x + y 8 x 0 y 0 A) Maximum of 32 when x = 3 and y = 2 B) Maximum of 32 when x = 2 and y = 3 C) Maximum of 24 when x = 4 and y = 0 D) Maximum of 52 when x = 4 and y = 4 E) None of the above 3) _________ z =6 x +7 y 2 x +3 y 12 2 x +y 8 x 0 y 0 That is: 2 x +3 y =12 2 x +y =8 x =0 y =0 solve; 2 x +3 y =12 2 x +y =8 x =3, y =2 if ( 3, 2 ) , z =6 x +7 y z =32 4) A college student can spend no more than 8 hours a week tutoring. She charges $10 an hour to tutor finite math and $13 to tutor algebra. She limits herself to no more than 3 hours per week to tutor algebra and spends at least 1 hour a week tutoring each subject. How many hours per week should she spend tutoring each subject to maximize her income? What is her maximum weekly income? 4) _________ Hint: Let x = number of hours per week to tutor finite math and y = number of hours per week to tutor algebra Then use graphical methods to solve the following linear programming problem: Maximize z = 10x + 13y Subject to: x + y 8 y 3 x 1 y 1 A) 4 hours of finite math and 4 hours of algebra; maximum income is $92 per week B) 7 hours of finite math and 1 hour of algebra; maximum income is $83 per week C) 5 hours of finite math and 3 hours of algebra; maximum income is $89 per week D) 3 hours of finite math and 5 hours of algebra; maximum income is $95 per week E) None of the above z =10 x +13 y x +y 8 y 3 x 1 y1 That is; z =10 x +13 y x +y =8 y =3 x =1 y =1 If y =3 then x +3 =8 x =5 ( 5,3) If x =1 then 1 + y =8 y =7 ( 1, 7 ) If y =1then x +1 =8 x =7 ( 7,1) At ( 5,3) , z =10 x +13 y z =89 At ( 1, 7 ) , z =10 x +13 y z =101 At ( 7,1) , z =10 x +13 y z =83 Max z =101 At ( 1, 7 ) 5) Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, C = {v, w, x, y, z}. Find the elements in the set A B' 5) _______ A) {t, v, x} B) {u, w} C) {r, s, t, u, v, w, x, z} D) {q, s, t, u, v, w, x, y} and E) None of the above U = { q, r, s, t, u, v, w, x, y, z} , B =U - B ={ q, r , s, t, u, v, w, x, y, z} - B = { q, s, y, z} ={ r, t, u, v, w, x} A B ={ q, s, u, w, y} { r, t, u, v, w, x} ={ u, w} 6) Use the counting formula to solve the following problem. If n(B) = 12, n(A B) = 3, and n(A B) = 21, find n(A). 6) _______ A) 12 B) 14 C) 9 D) 10 E) None of the above n ( A B ) =n ( A ) +n ( B ) - n ( A B ) 3 =n ( A ) +12 - 21 3 =n ( A ) - 9 n ( A ) =12 7) If n(A) = 32, n(B) = 93 and n(A B) = 109, what is n(A B)? A) 8 B) 18 C) 48 D) 16 7) _______ E) None of the above n ( A B ) =n ( A ) +n ( B ) - n ( A B ) =32 +93 - 109 =125 - 109 =16 Solve the following problems. 8) At East Zone University (EZU) there are 897 students taking College Algebra or Calculus. 520 are taking College Algebra, 450 are taking Calculus, and 73 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? 8) _______ A) 824 B) 374 C) 377 D) 447 E) None of the above n ( A ) =520 n ( C ) =450 n ( A C ) =897 n ( A C ) =73 n ( eople taking Calculus but not algebra ) =450 - 73 =377 9) A restaurant offered salads with 8 types of dressings and 4 different toppings. How many different types of salads could be offered? 9) _______ A) 32 types B) 16 types C) 12 types D) 64 types E) None of the above 8 4 =32 10) How many ways can a committee of 5 be selected from a club with 10 members? 10) ______ A) 30,240 B) 252 C) 50 D) 100,000 E) None of the above n! ( n - r ) ! r ! = 10! ( 10 - 5 ) ! 5! 10! 5! 5! 6 7 8 9 10 = 5! 6 7 8 9 10 = 1 2 3 4 5 6 7 8 9 = 3 4 =2 7 2 9 =252 =