Identify a pattern in the list of numbers. Then use this pattern to find the next number. 1) 37, 31, 25, 19, 13

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1 Math1001 Final Exam Review Identify a pattern in the list of numbers. Then use this pattern to find the next number. 1) 37, 31, 25, 19, 13 Which reasoning process is shown in the following 2 examples? 2) We examine the social security numbers of 100 people. No two individuals from this group of people have identical social security numbers. We conclude that for all people, no two people have identical social security numbers. 3) If Mary goes to the mall, she gets ice cream. Mary did not get ice cream. We conclude Mary did not go to the mall. Solve the problem with estimation, but do not use a calculator. Use rounding to make the resulting calculations simple. 4) You spend $41.28 for a meal. If you want to leave a 15% tip, estimate the amount of the tip. The line graph above shows the price of a stock over the course of the day. Use the graph to answer the question(s). 5) At what time was the stock price highest? Use the four-step method in problem solving to 6) A couch sells for $1260. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $80 a month for 12 months. How much is saved by paying the total amount at the time of purchase? 7) A certain Internet provider charges for 150 hours of online usage per month and for each additional hour. If Marc was online for 200 hours last month, what was his bill for that month?

2 Use dimensional analysis to convert the quantity to the indicated units. If necessary, round the answer to two decimal places. 8) 10 yd to in. 9) 2.56 m to cm 10) mm to m 11) A race track is 540 meters long. If a driver goes around the race track twice, how many kilometers did the driver travel? 12) 9 in. to cm 13) 271 km to mi The bar graph below represents various colors of cars sold. Use the graph to answer the question(s). 14) Which color sold over 50,000 cars?

3 Use dimensional analysis to convert the given square unit to the square unit indicated. Where necessary, round the answer to two decimal places. 15) 6m 2 to km 2 16) A television set has an area of 169 square inches. How many square feet is this? 17) 924 in 3 to gal Convert the given unit of weight to the unit indicated. 18) 164 mg to g 19) Which is more economical: purchasing the economy size sack of beans at 7 kilograms for $12, or purchasing the regular size bag at 58 grams for $1.40? 20) 820 lb to kg 21) For each kilogram of a person's weight, 60 milligrams of a drug is to be given. What dosage should be given to an adult who weighs 170 pounds? Convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. Where appropriate, round to the nearest tenth of a degree. 22) 107 F Use similar triangles to 23) A flagpole casts a shadow of 36 ft, Nearby, a 10-ft tree casts a shadow of 3 ft. What is the height of the flag pole? 24) If you drive 5 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? 25) A garden is in the shape of a rectangle 47 feet long and 25 feet wide. If fencing costs $7 a foot, what will it cost to place fencing around the garden?

4 26) What will it cost to tile a rectangular floor measuring 255 feet by by 28 feet if the tile costs $16 per square foot? 27) How much fencing is required to enclose a circular garden whose diameter is 287 m? 28) A 7-inch circular apple pie sells for $4. What is its cost per square inch? Round to the nearest cent. Graph the equation. 29) y = 1 6 x - 3 Evaluate the function at the given values of the variable. 30) f(x) = 3 + 9x + 1 a. f(-3) b. f(-5)

5 The figure shows the percentage of the U.S. population, f(x), made up of teachers as a function of time, x, where x is the number of years after Use the graph to 31) Use the graph to estimate f(50). 32) The monthly cost of a certain texting plan is given by the function C(n) = 0.05n , where C(n) is in dollars and n is the number of texts sent in a month. Find and interpret C(60) Monthly Cost of Texting Plan

6 33) The linear function I(t) = 775.8t + 24,269 can be used to model the average annual income for single mothers as a function of t, where t represents the number of years since year 0. Interpret the slope. 34) Linda needs to have her car towed. Little Town Auto charges a flat fee of $80 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 5 miles. 35) The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells flat-screen TVs. Use the formulas shown to find R(300) - C(300). Describe what this means for the company.

7 36) A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $90 for the truck and $45 per hour for the movers. Company B charges $80 for the truck and $50 per hour for the movers. Create a cost equation for each company where y is the total cost and x is the number of hours of labor. Write a system of equations. 37) The exponential function P=7(1.03) x describes the price P, in dollars, of a movie ticket in a local cinema in year x, assuming a yearly inflation rate of 3%. What was the original ticket price (year 0)? What will the price be in year 9? 38) The cost, in millions of dollars, for a company to manufacture x thousand automobiles is given by the function C(x) = 5x 2-40x+144. Find the number of automobiles that must be produced to minimize cost. 39) As part of a fundraiser, a local charity has sold 5 raffle tickets, with a goal of selling 30 tickets. What percentage of the goal has been sold? (Round to the nearest tenth of a percent, if necessary.)" 40) Suppose that the luxury sales tax rate in a foreign country is 29%. A very wealthy socialite bought a diamond tiara for $185,000. How much tax does she pay? The graph shows the level of subsidized daycare spending in a foreign country for the period Use the graph to answer the question. 41) Find the percent increase in daycare spending from 1995 to Round to the nearest percent.

8 The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. 42) P = $700.00, r = 5%, t = 8 months Determine the present value, P, you must invest to have the future value, A, at simple interest rate r after time t. Round answer to the nearest dollar. 43) A = $204.80, r = 7%, t = 4 years The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years (Assume 360 days in a year.), and how much interest was earned. 44) Principal: $8000 Rate: 6% Compounded: quarterly Time: 3 years 45) A mother invests $9000 in a bank account at the time of her daughter's birth. The interest is compounded quarterly at a rate of 7%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? 46) James and Susan wish to have $10,000 available for their wedding in 4 years. How much money should they set aside now at 6% compounded monthly in order to reach their financial goal?

9 Find the value of the annuity and the interest. Round to the nearest dollar. 47) Periodic Deposit: $50 at the end of every month Rate: 4.25% compounded monthly Time: 9 years Determine the periodic deposit. Round up to the nearest dollar. How much of the financial goal comes from deposits and how much comes from interest? 48) Periodic Deposit: $? at the end of every six months Rate: 6% compounded semiannually Time: 8 years Financial Goal: $490,000 49) Suppose that you decide to buy a car for $25,485, including taxes and license fees. You saved $7000 for a down payment and can get a five-year loan at 6.52%. Find the monthly payment and the total interest for the loan. 50) The price of a home is $330,000. The bank requires a 5% down payment. After the down payment, the balance is financed with a 20-year fixed-rate mortgage at 8%. Determine the monthly mortgage payment (excluding escrowed taxes and insurance) to the nearest dollar. 51) You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?

10 52) A restaurant offers a choice of 4 salads, 8 main courses, and 4 desserts. How many possible meals are there? 53) In a contest in which 10 contestants are entered, in how many ways can the 4 distinct prizes be awarded? 54) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded? 55) A record club offers a choice of 7 records from a list of 45. In how many ways can a member make a selection? 56) In how many ways can a committee of three men and four women be formed from a group of 10 men and 10 women? 57) A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss. 58) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 4 or 2. 59) Six people from different occupations were interviewed for a survey, and their annual salaries

11 were as, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the mean annual salary for the $12,000 six people? 60) Six people from different occupations were interviewed for a survey, and their annual salaries were as follows $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the median annual salary for the six people? Find the mode for the group of data items. 61) 97, 97, 94, 47, 71, 97 If there is no mode, so state. Compute the mean, range, and standard deviation for the data items in each of the three samples. Then name one way in which the samples are alike and one way in which they are different. 62) Sample A: 11, 13, 15, 17, 19, 21, 23 Sample B: 11, 14, 14, 17, 20, 20, 23 Sample C: 11, 11, 11, 17, 23, 23, 23 Find the a. mean and b. standard deviation for the data set. Round to two decimal places. 63) International Travel Destinations of U.S. Citizens