Unit I q5. Factor the following natural number. If the number is prime, state so 114 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. The prime factorization is (Type your answer in factored form.) b. The number is prime Unit1q7. Find the GCD and LCM of the following pair of natural numbers.20,88 a. The GCD of 20 and 88 is . (Type a whole number.) b. The LCM of 20 and 88 is (Type a whole number.) Unit Iq7b.Find the GCD and LCM of the following pair of natural numbers.63, 297 The GCD of 63 and 297 is (Type a whole number.) Unit Iq9. Two people are jogging around a circular track in the same direction. One person can go completely around the track in 14 minutes. The second person takes 20 minutes. If they both start running in the same place at the same time, how long will it take them to be together at this place if they continue to run? They will be together again after minutes Unit Iq15. Write the following division problem as a corresponding multiplication problem and then solve it.+15 +5 Which of the following is the corresponding multiplication problem for +15? +5 = c ? A.+5=(+15)c B. +15=(+5)c C. c=(+5)(+15) Unit Iq25. Write the fraction in lowest terms.24 32 24 / 32= (Simplify your answer. Type an integer or a fraction.) Unit Iq28. Perform the calculation. Express the answer as a positive or negative quotient of two integers in reduced form. 1/82/3+1/2. 1/82/3+1/2. = or a fraction.) (Simplify your answer. Type an integer Unit Iq30. Perform the following operations. Express your answer as a positive or negative quotient of two integers in reduced form. 46 105 ( 1 7) 21 138 46/105 divide (1/12 - 7/138) = Type an integer or a simplified fraction Unit Iq31. Write the improper fraction as a mixed number in simplest form. 30 over 7 30 over 7= (Simplify your answer. Type a mixed number.) Unit Iq32. Write the improper fraction as a mixed number in simplest form. 149 149 13 13 = (Simplify your answer. Type a mixed number.) Unit Iq34. Find a decimal representation of 23 Over 33 23 Over 33 =0. (Type only the first block of digit(s) that repeat.) Unit Iq35. Express the given terminating decimal as a quotient of integers. If possible, reduce to lowest terms 0.57 0.57 =? Q36. Instructions:A mix for 11 servings of instant potatoes requires 1 and three eighths138 cups of water. Use this information to decide how much water is needed if you want to make 15 servings. The amount of water needed to make 15 servings is cups. (Type an integer, proper fraction, or mixed number.) unit II q12. Summarized on the right is the sale (in thousands) of the top five products in 2002. Use this information to calculate what percent of the sales of these five products was due to product D. of the sales of these five products was due to product D.(Round to the nearest hundredth as needed.) Qtn 21. Use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $2,500 is deposited in an account at an annual interest rate of 5% and the interest is compounded daily. (Assume there are 365 days in a year.) The amount after 10 years will be $ (Round to the nearest cent as needed.) Unit II 28. Angela's bank gave her a 2year addon interest loan for $5,090 to pay for new equipment for her antiques restoration business. The annual interest rate is 10.44%. How much interest will she pay? What are her monthly payments? She will pay $ in interest on the loan. (Round to the nearest cent.) Unit II 29. Using the unpaid balance method, find the current month's finance charge on a credit card account having the following transactions. Last month's balance: $625 Last payment $120 Annual Interest rate: 18% Purchases 399 Returns: $414 The finance charge is $ (Round to the nearest cent.) Unit II 30. Use the average daily balance method to compute the finance charge on the credit card account for the month of August (31 days). The starting balance from the previous month is $280. The transactions on the account for the month are given in the table to the right. Assume an annual interest rate of 22% on the account and that the billing date is August 1st. Date Transaction August 7 Made payment of $71 August 13 Charged $140 for hiking boots August 22 Charged $27 for gasoline August 26 Charged $25 for restaurant meal The finance charge for the month of August is $ . (Round to the nearest cent as needed.) Unit II 31. Find the APR of the loan given the amount of the loan, the number and type of payments, and the addon interest rate. Loan amount, $6,000; three yearly payments; rate=8% The annual percentage rate is (Type an integer or a decimal.) Unit 32. Find the finance charge per $100 for the loan described below. Loan, $2,400; finance charge, $384. The finance charge is $ per $100. Unit II 33. Luisa pays a finance charge of $152 on a 6month, $3,700 loan. Find the annual percentage rate using the annual percentage rate table APR 10% 11% 12% 13% 14% 15% 16% Number of Payments Finance Charge per $100 $2.94 $3.23 $3.53 $3.83 $4.12 $4.42 $4.72 6 12 $5.5 $6.06 $6.62 $7.18 $7.74 $8.31 $8.88 0 24 $10.7 $11.86 $12.98 $14.10 $15.23 $16.37 $17.51 5 36 $16.1 $17.86 $19.57 $21.30 $23.04 $24.80 $26.57 6 48 Annual Percentage Rate Table $21.7 $24.06 $26.40 $28.77 $31.17 $33.59 $36.03 4 The annual percentage rate is (Round to the nearest integer as needed.) Unit II 34. Estimate the annual percentage rate for the addon loan using the given number of payments and annual interest rate. Use the formula APR 2nr Over n plus 1 n=42; r=7% APR (Round to two decimal places as needed.) Unit III 11. Simplify by rationalizing the denominator. 2 5 The answer is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Unit III 17. The equation D = 2H approximates the distance D, in miles, that a person can see to the horizon at a height of H feet. How many miles could a forest ranger see to the horizon if his eyes are 6 feet above footlevel and he is standing on a fire tower that is 294 feet high? Express the answer as a radical expression and then as a decimal. First express the answer as a radical expression. The forest ranger could miles to the horizon (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Unit III 22 2 . Multiply.6 6 3 = 6 Unit III 28. Convert to decimal notation. 9.3410 = 2 4 nit III 30. Multiply and write the result in scientific notation. (2 10 )(310 ) 2 4 (210 )(310 )= (Simplify your answer. Use scientific notation. Use the multiplication symbol in the math palette as needed.) Unit iii 34. Identify the sequence as either arithmetic or geometric. List the next two terms of the sequence. 2, 1/4, 1/32, 1/256, ... Is the sequence arithmetic or geometric? Unit iii 35. For the following arithmetic sequence: a) find the specified term an and b) find the sum of the terms from a1 to an, inclusive. 4, 6, 8, 10,...; find a10. find a10.= Unit iii 40. Given the two terms in the Fibonacci sequence shown below, find the specified term. F37=24,157,817, F38=39,088,169, find F36 Unit vi 9. If the odds against a particular soccer team winning a soccer tournament are 9 to 5, what is the probability that they will win the tournament? The probability that the soccer team will win the tournament is (Simplify your answer.) Unit vi 21. We are drawing a single card from a standard 52card deck. Find the following probability. P(nine | nonface card) The probability is (Type an integer or a simplified fraction.) Unit vi 28. Imagine a subject is taking part in a study to test a new cold medicine. The probability that the subject is taking drug A is 10%, that it is drug B is 20%, and that it is drug C is 70%. From past clinical trials, the probabilities that these drugs will improve his condition are A (20%), B (50%), and C (80%). What is the probability that he will improve? The probability is (Type an integer or decimal) Unit vii 1. The following data represent the number of potholes on 35 randomly selected 1mile stretches of highway around a particular city. Construct a frequency table, a relative frequency table, and a bar graph for the data. Number of Potholes 1 7 1 7 1 1 3 4 5 2 1 5 5 2 3 1 1 6 4 3 4 1 3 1 2 4 5 1 3 6 1 7 1 2 3 Construct a bar graph for the data. Choose the correct graph below. A. On horizontal axis are 1 2 3 4 5 6 7 on vertical axis are 0 4 8 1 2 B, C, D Unit vii 15. A group of 20 students were asked how many times they visit a certain website per week and the following results were obtained. Find the mean, median, and mode for the distribution.9, 4, 17, 4, 13, 11, 21, 20, 21, 27, 6, 19, 25, 21, 12, 10, 1, 23, 18, 4 A. The mean is (Type an integer or decimal rounded to one decimal place as needed.) B. There is no mean for these data. Unit vii 18. A college placement office has made a comparative study of the starting salaries for graduates in various majors. The following boxandwhisker plots describe the starting salaries for business, education, engineering, and liberal arts. Does liberal arts or education have the higher median salary? Does this imply that salaries in liberal arts are generally higher than those in education? a. Does liberal arts or education have the higher median salary? b. Do the results imply that salaries in the major with the higher median salary are generally higher than those in the major with the lower median salary? Unit vii 21. Find the mean and standard deviation of the frequency distribution x 2 3 4 5 6 f 2 3 3 0 1 The mean is approximately what is the standard deviation? (Round your answer to two decimal places.) \f\f\fUnit iv.2 Lines L and M are parallel. Determine which of the lettered angles are alternate interior alternate interior angles A.x k B.y and h C.w and h D.x and n E.k and w F.w and n Unit 1. 21 The area is cm2.(Type an integer or a decimal.) Unit iv.2 Lines L and M are parallel. Determine which of the lettered angles are alternate interior alternate interior angles A.x k B.y and h C.w and h D.x and n E.k and w F.w and n Unit 1. 21 The area is cm2.(Type an integer or a decimal.)