Math 110 Supplemental Handbook - PBworks



Math 110 Supplemental HandbookFall 2017DISCLOSURES PAGE*Some practice problems for the Select Examples and Study References sections was pulled from CK-12: *Some content for the Select Examples and Study References sections was pulled from: Arithmetic for College Students by David Lippman: ?*Additional Course resources such as lessons, extra worksheets, extra labs, and videos?can be found at:? mat110opensource.*The handbook was written and put together by Chelsea Smith with the Select Examples section and some Study References from Lee Wilsonwithers.*This handbook is to function as a supplemental resource for Math 110 with the primary teaching of the course coming from each individual instructor. The Story Behind the Cover: As an instructor of Math 110 since I began teaching at Forsyth Technical Community College, it has easily become one of my favorite courses to teach. As the class has evolved over the years I have seen a few different textbooks used for the course, but through a community effort to decrease the cost of textbooks to students I began putting together a handbook that would function as an assisted learning tool for students taking Math 110, at a fraction of the price of a textbook. The picture on the front of the handbook is in the shape of an octagon, for I have always taken the number eight as a symbol of luck. Hopefully the knowledge you attain from this course will bring you luck and help you in attaining the goals you hope to achieve.~Chelsea Smith LegendWorksheet TopicPagePercentages5-6Additional Percent Problems7-8Real World Percent Problems9-10Ratios and Proportions11-12Additional Applications of Ratios and Proportions13-14Probability15-16Measurements17-18U.S. Conversions19-20Metric Conversions21-22Temperature23Angle Measurements25-27Perimeter and Area of Polygons and Quadrilaterals29-31Perimeter and Area of Triangles, Hexagons and Irregular Polygons33-35Circles37-39Volume and Surface Area41-43Interpreting and Constructing Graphs45-47Measures of Central Tendency49-51Measures of Dispersion53-54Normal Distributions55-56Simple and Compound Interest57-58Loans and Credit Cards59-60Annuities61-62LAB #163-65LAB #266-69LAB #370-76LAB #477-78LAB #579-80Study References81-87Review Questions88-94Select Examples95-103The following asterisk * seen at the end of a question means to round the answer to the question to the nearest tenth unless otherwise specified.Percentages WorksheetConvert the following decimal in #1-3 to a percent.3.75b) 4.340.675b) 0.0230.001b) 0.89Convert the following percent in #4-6 to a decimal.45%b) 2.1%0.3%b) 45.5%1214%b) 0.0023%Rewrite the following percentages in # 7-10 as a fraction in lowest terms.42%b) 12%37.5%b) 13%175%b) 24%64%b) 72%Additional Percent Problems WorksheetWhat percent of 35 is 2.5? *45 is 15% of what number?9 is what percent of 120?40% of what number is equal to 15?If you answered 35 out of 45 questions correctly on your math exam, what grade would you make? *The manager of a restaurant is in charge of ordering produce for the restaurant every evening. If the restaurant needs 26 pounds of asparagus for the evening meal but he expects that only 80% of the asparagus delivered will be good, what is the minimum amount of asparagus that the manager will need to order?If you made $25 an hour and then got a 3% raise, how much do you now make per hour?If sales tax is 7%, what is the price of an object before tax if you paid $7.80 in tax?A store buyer purchased 612 dozen blue T-shirts and 214 dozen red T-shirts. What percent of the order consisted of red T-shirts? *Round your answer to the nearest whole percent.If 6% of your salary is withheld for Social Security and after Social Security is taken out they take 15% of what is left out for taxes, how much will you take home if you made $3,000 this month before anything was taken out?Real World Percent Problems WorksheetIf a laptop costs $1200 and you paid $102 in sales tax, what was your sales tax rate?Sally is a car sales person and she makes commission on all of the cars that she sells. If Sally sold $765,987 worth of used cars last year and she makes 3% commission on all sells, how much money did Sally take home last year?If a Barbie was $0.55 in 1970 and is now worth $10.45, what percent increase did Barbie experience over the 46 year period?You went to the mall and bought the following items: A shirt for $32, a pair of pants for $65 (which was 15% off), a pair of socks for $10 and a hat for $18. If you had to pay 6.75% sales tax on your total purchase how much did you pay for all the items?If your car was worth $32,000 when you bought it 3 years ago but since then it has experienced a 23% decrease in value, how much would your car be worth today?If you bought a pair of jeans for $42 that were 20% off, but then you had to pay 7.25% sales tax, how much will the cashier charge you for the jeans?If you invested $3,000 at 8% interest for 24 months, how much would you have in your account after the 24 month period? Following question #7, how much interest have you earned on your investment after the 24 month period?When you last went to get your car inspected the mechanic told you that your engine was running at 75% efficiency. If your car is supposed to output 85 horsepower, how much horsepower is your engine actually giving off? An outdoor BBQ at Home Depot was priced at $1,250, but you only paid $875. What percent discount did you receive on the BBQ? Ratios and Proportions Worksheet6X=304017=16X212X=1143120.115=2XIf 32 pins can be made from a 12 foot steel rod, how many pins can be made from a steel rod that is 9 feet long? You work for a processing plant that ships boxes of cookies. If you can produce 12 boxes of cookies in 40 minutes, how many boxes can you produce in 6 hours? In the election for school president Sarah won by a vote of 6 to 5. If Sarah received 822 votes, how many votes did her competitor receive?If you can harvest 150 bundles of hay in 3 hours, how many bundles of hay can you harvest in a day? If it took you 212 days to paint 13 of your kitchen cabinets, how many days would it take you to paint all your kitchen cabinets? If a bottle of Advil contains 3000 milligrams of medicine and contains 50 pills, how many milligrams of medicine would 2 pills contain? Additional Applications of Ratios and Proportions WorksheetIf 50 gallons of oil can flow through a pipe in 25 minutes, how long will it take 525 gallons of oil to flow through the same pipe?The width of a room to the length of a room is 3.25 to 2. If the width of a room is 15 feet, find the length of the room. *The volume of a cylinder is inversely proportional the pressure of a cylinder. If a gas has a volume of 2400 cu cm at a pressure of 65 psi, what is the pressure when the gas is compressed to 1850 cu cm? * If you got paid $225.50 for 22 hours of work, how much should you get paid for working 37 hours at the same rate? If Sam is 6 feet tall and casts an 8 foot shadow, how tall is a nearby house that casts a 20 foot shadow? Three hundred workers can produce 550 widgets at a factory plant. On New Year’s Day, the amount of workers is cut down to 75 people. Given this amount of people, how many widgets can the factory produce on New Year’s Day? *Round to the nearest whole number of widgets.You know that it takes you 5.5 hours to go to your grandmother’s house driving 55 miles per hour. If the speed limit signs were just changed on the highway and you can now travel 65 miles per hour, how long will it take you to get to grandmother’s house? How far away is your grandmother’s house? * Round to the nearest tenth of an hour.You work 8 hours a day at a retail store where you make $7.55 an hour for the first and last hour you work setting up and cleaning up, but then you make $10.50 an hour while working with customers the rest of the day. If you work 5 days a week, how much do you make each week before taxes? Find the missing side length in the similar figures below:15 in6 in2 inX15 in6 in2 inX In a cereal factory 30 employees can box up (on average) 12 boxes of cereal a minute. If a new machine that is brought in can box 15 boxes of cereal a minute, how many machines would it take to replace the 30 employees? ProbabilityPut all your answers as fractions in lowest terms.Find the probability of rolling a six-sided dice and getting an odd number. You randomly pick a pair of socks out of your drawer every morning. If you have 4 white pairs, 5 black pairs and 6 colored pairs of socks in your drawer, find the probability of randomly picking out a black pair of socks. Find the probability of rolling a six-sided dice and getting an eight. If you randomly pick a card out of a standard deck, what is the probability you will draw a Heart? If you randomly pick a card out of a standard deck, what is the probability the card will not be an 8? On a recent survey of all Math 110 students favorite flavor of ice cream 45 people said they prefer chocolate ice cream, 32 said vanilla ice cream and 18 said other. If you randomly asked a student in Math 110 what their favorite flavor of ice cream was find the probability of asking someone who says chocolate ice cream. Find the probability of randomly picking an Ace of Spades out of a standard deck of cards. Find the probability of not picking an Ace of Spades out of a standard deck of cards. From a standard deck of cards find the probability of randomly drawing a Queen and then without replacing your first card randomly drawing a Jack. If you roll a quarter and it comes up Heads the first time, what is the probability you will roll Heads the second time? Three cards are chosen at random without replacement from a standard deck of cards, find the probability of choosing three Kings in a row. Measurements Worksheet24 miles ÷ 1.5 hours70 ft ÷ 35 ft/secIf a rectangular floor has an area of 672 square feet and has a width of 24 feet, what is the length of the room? If a plane traveled 2700 miles going 600 miles per hour how many hours was the plane in flight? Round 14.56 to the nearest tenth.Round 123.7845 to the nearest hundredth. 12.582 minutes – 8.751 minutes15.235 hours – 240 minutesIf a crate full of fruit weighs 23.67 lbs and the fruit alone weighs 18.68 lbs, how much does the crate weigh?Round 123.7845 to the nearest hundred.U.S. Conversions WorksheetFor number 1-5 perform the proper conversion:8.75 feet to inches50 lbcu ft to lb cu in *Round your answer to the nearest hundredth.3.5 gallons to cups13 square feet to square yards.* 543 revolutions per second to revolutions per minuteIf you must cut 12 strips of metal and each strip of metal is 2 feet 7.5 inches, how many inches of metal are required to cut all 12 strips? A patient is required to drink 14 quart of liquid every 2 hours. How many cups of liquid would this patient be required to drink in a week? If you paid $18.35 for 2 pounds of chocolate, how much did you pay per ounce of chocolate? A woman must decide to drive or take the subway to work. If the woman lives 24.3 miles from work, a monthly subway pass costs $55, her car gets 27 miles per gallon, the cost of a gallon of gas is $3.75 per gallon and the woman drives to work 20 days a month, would it be cheaper for the woman to drive or take the subway? How much would the woman save if she took the cheaper mode of transportation to work? If you need 312 cups of flour for every batch of chocolate chip cookies you make, how many pints of flour will you need if you have to make 7 batches of cookies?Metric Conversions WorksheetConvert 3.45 g to kgConvert 0.98 cm to mmConvert 2.4 ft/sec to m/hr*The density of steel is ~ 8 gcm3. Express this number as grams per cubic foot. (1 foot ~ 30.5 cm) If a plane can travel at an average speed of 550 mph, how fast can a plane travel in km/min? *A man weighing 190 pounds should not consume more than 912 calories a day from fat. If a gram of fat contains 8 calories, what is the maximum number of grams of fat this man should consume? Review last section: If a chocolate chip recipe calls for 212 cups of flour per batch and you need to make 6 batches of cookies, how many quarts of flour do you need to make all the cookies. 8 cm = _____ inches* If a 5 km race ~ 3.1 miles, how many km would you have to run to complete a 26.2 mile marathon? *According to many dietary plans people are supposed to consume 8-8 ounce glasses of water a day. If there are 33.814 fluid ounces in a liter, how many mL of water would an average dietary plan suggest you consume in a day? *Temperature ConversionsConvert 85°F to Celsius.* Convert 13°C to Fahrenheit.Convert 35°F to Celsius.*Find -7°C to Fahrenheit.Find the temperature of boiling water in Fahrenheit and Celsius.Find the temperature of freezing water in Fahrenheit and Celsius.Find a location in the world that uses Celsius temperature in their daily lives. Angle Measurements WorksheetFind the missing angle in the triangle below:67°54°67°54°Find the missing angles a-g in the figure below.82°abcdefg82°abcdefgIf a right triangle has one angle that measures 42° what is the measurement of the other two angles in the triangle? Find the missing angle in the diagram below:110°110° Angle A is a corresponding angle to angle B and angle B and angle C make up a right angle and angle C and angle D are alternate interior angles. If angle A measures 54°, what is the measure of angle D?Classify the following angles as acute, right or obtuse and find the supplement angle for each. 143° b) 90° c) 25° d) 179°Fill in the blanks. The point of intersection between two lines is called a _______. When two lines intersect the measure of the opening is called an _____. When two parallel lines are intersected by a third line, this third line is called a _______. When two angles add to 90°, the two angles are called_____. When two angles add to 180°, the two angles are called ______.Fill in the missing angles in the following diagram. 140°30°abc140°30°abcFill in the missing angles in the following diagram. 65°a°b°c °d °e °f °g °h °65°a°b°c °d °e °f °g °h ° Find the missing angle in the following triangle: 63°58°63°58°Perimeter and Area of Polygons and Quadrilaterals WorksheetFor the figures in #1-3 below find the perimeter and area of the figure. Be sure to include units. 12 yd14 yd18 yd13 yd11 yd12 yd14 yd18 yd13 yd11 yd*How many squares are in the figure below? Then find the area of each square.320 m275 m198 m121 m82 m320 m275 m198 m121 m82 mIf the den in your house is 12 feet by 19 feet and the whole room is to be carpeted, how many square yards is your den? In addition, if carpet cost $35.99 per square yard how much will it cost you to carpet your den? *A roll of carpet padding is 18 inches wide. What length of padding is required to obtain 15 square feet of material? If a particular copper plated sheet weights 2.75 lbs per square foot, how much would a piece of this copper plated sheet weigh if the sheet is 36 inches by 100 inches? You want to tile your kitchen floor which is 16 ft by 12.5 ft. If each tile is 12 in by 12 in, how many pieces of tile will you need to buy to cover your entire floor if you need to order an extra 20% to allow for mistakes and end pieces? Your yard is in the shape of a trapezoid with side lengths of 15 yards and 21 yards, bases of 18 yards and 39 yards and a height of 18 yards. If you want to plant grass seed in your yard and each bag of grass seed will cover 225ft2, how many bags of grass seed will you need to cover your whole yard in grass seed? How many squares with 9 meter side lengths can you fit into a parallelogram with a base of 27 meters and a height of 18 meters?Perimeter and Area of Triangles, Hexagons and Irregular Polygons WorksheetFind the height and area of a triangle with a base of 24 inches and two side lengths of 18 inches. *Find the area of a hexagon where the distance across the corners is 10 meters. Find the area of the shaded region below if the exterior equilateral triangle has a side length of 4.2 cm and the interior equilateral triangle has a side length of 2.7 cm. *If the base of a right triangle is 14 inches and the area of the triangle is 42 in2, what is the height of the right triangle? Find the hypotenuse of a right triangle if the base of the triangle is 8 inches and the height of the triangle is 7 inches. You are getting your driveway resurfaced this summer with concrete blocks in the shape of regular hexagons. If your driveway measures 10 ft by 30 ft and each concrete block is 8 inches across the flats, how many blocks will you need to completely resurface your driveway? Be careful to interpret any remainders.Find the area of the following triangle*:18 m21m18 m21mFind the area of the following figure (which may not be drawn to scale) given that the triangle is an isosceles triangle and the shape on the end is a square.14yd19 yd12.5 yd14yd19 yd12.5 ydA driveway is going to be poured in the shape below. If 14 bag of concrete is required per square yard, answer the following questions. *Hint: Your driveway consists of a square and a rectangle. 13.5 yd31 yd27 yd13.5 yd31 yd27 ydWhat is the total area of driveway you will need to pour?Based on the diagram above, how many bags of concrete will you need to pour the driveway? Think about how to interpret the remainder.If concrete costs $2.88 per bag, how much will it cost you to pave the driveway pictured?Find the area of the following figure below*:14 in14 in18 in8 in24 in17 in18 in14 in14 in18 in8 in24 in17 in18 inCircles WorksheetFor the following questions you can use π ~ 3.14. Round all answers to the nearest tenth if it doesn’t come out to a whole number and be sure to include units.Find the area and circumference of a circle with a diameter of 15 meters.Find the area and circumference of a semicircle with a radius of 7 cm. A small pizza at Dominos is 10 inches in diameter, whereas a medium pizza is 13 inches in diameter. If a small pizza serves 4 customers, how many customers will a medium pizza serve (assume each customer gets the same amount of pizza whether they eat a small or medium pizza). *Round up to the nearest person. Find the area of a washer (annulus) that has an inner radius of 8 cm and an outer radius of 11 cm. Below is a window in your new home, find the area and perimeter of the window. Given the window in #5, if you wanted to put molding around the window and straight molding cost $2.75 per foot and curved molding cost $3.50 per foot, how much would it cost you to put molding around the whole window? (1 ft ~ 0.3 meters)Find the area of the following figure below:Find the area and perimeter of the following figure:You are working on constructing manholes to cover water lines in your neighborhood. If you need the manholes to have a circumference of at least 95 inches, how many feet wide must the manhole be? *Round your answer to the nearest tenth of a foot.Find the length of stock needed to create an annulus that has an inner diameter of 7 inches and an outer diameter of 9 inches. Volume and Surface Area WorksheetFind the volume and surface area of the figures in #1-4 below. Use 3.14 for pi.10 cm5 cm10 cm5 cmA cylinder with a height of 50 cm and a radius of 40 cm with a cone on top of the cylinder. The cone has a height of 30 cm. It might help to draw the figure before finding the volume and surface area. Keep in mind for surface area that the cone is sitting right on top of the cylinder.Sphere with a radius of 30 meters.8 m3 m5 m8 m3 m5 mYou go to Ben and Jerry’s to get some ice cream but you have to make a choice. If both of the following options cost the same amount, which one would be a better deal? You can either get a bowl of ice cream with two scoops, scooped from a 1.75 inch scoop or you can get one scoop of ice cream scooped from a 2.8 inch scoop. Assume the scoops of ice cream are perfect spheres. You are throwing a Christmas party and want to figure out how many cups of juice you have already made. If your punch bowl is in the shape of a half sphere with a radius of 8 inches and your ladle is in the shape of a half sphere with a radius of 1.5 inches, how many ladles of juice can you get out of your punch bowl? Assume that the punch bowl and ladles are full. *Round down to the nearest whole number of ladles.How many cubic inches are in a cubic yard?What is the volume of an irregular figure that has an area of 55 square feet and a height of 3 feet?You go to buy a birthday cake for your son’s 12th birthday but you want to get the most cake for your money. If both of the following cakes cost the same amount, which cake is a better deal? A rectangular cake with a length of 12 inches, a width of 8 inches and a height of 5 inches, or a round cake with a radius of 8 inches and a height of 5 inches? In a cone which would cause the volume to increase by more: tripling the radius or tripling the height? Interpreting and Constructing Graphs WorksheetEach question is worth 2 questions.Answer the following questions based on the pie chart below: Given the pie chart above, what is this person’s total monthly budget per month? What percent of this person’s monthly budget comes from rent? ($750) *Round to the nearest whole percent.Given the pie chart above, how much would this person spend on school bills ($250 per month) for a whole academic year (9 months)?Calculate the percent increase in the amount of money spent on groceries ($250) as opposed to eating out ($100). Answer the following questions based on the line graph below:How much (per share) did the stock increase over the two week period?Find the overall percent increase of the stock value over the two week period.*Round your answer to the nearest whole percent.Did the stock gain or lose value in the first week? How much was the gain/loss?Between which two days did the greatest jump in stock value occur? Given the following data below, make a bar graph to properly display the data. Be sure to include a title, legend etc. Cause of FireNumber of FiresArson7Electrical Issues15Appliances6Gas9Vehicle Accidents7Unknown3Lighting Issues2Given the following data below, make a line graph to properly display the data. Be sure to include a title, legend etc. YearCost of Regular GasolineCost of Diesel Fuel20072.792.9220083.163.7220092.482.5720102.773.0020113.493.7720123.533.9320133.483.9020143.233.3520152.452.65Answer the following questions based on the double line graph below:For the following graph on the x-axis: 2000=1, 2001=2 etc. Top line: Sales. Bottom line: InventoryIn what year did the biggest gap between sales and inventory of homes occur?About how many homes were sold in 2003 as compared to 2006?Estimate the percent decrease in sales from 2000 to 2008.Estimate the percent increase in inventory from 2000 to 2002.Measures of Central Tendency WorksheetFind the mean, median and mode of the following set of numbers: 13, 15, 11, 19, 21, 22, 19, 18, 16, 12, 17, 10.*Find the mean, median and mode of the following set of numbers: 14, 18, 9, 21, 45, 67, 93, 18, 24, 65, 15, 85, 75, 64, 9. *Find the mean, median and mode of the following set of numbers: 45, 32, 75, 55, 48, 83, 90, 27, 36, 20, 68.*Below is a chart of the minimum hourly wage in a variety of states in the United States. Answer the following questions based on the chart below. (Worth 2 questions)StateMinimum Hourly WageNorth Carolina$7.25Oregon$9.75California$10.00Georgia$5.15New York$9.00Maine$7.50Michigan$8.50Florida$8.05Find the average minimum hourly salary of the eight states included in the chart.If the federal minimum wage in the USA is $7.25/hour, how much more would you make in a month (given 4 weeks in a month) in New York if you worked 40 hours a week, than if you were paid the federal minimum wage working 40 hours a week?By what percent does the minimum hourly salary of someone living in Oregon exceed that of the average minimum hourly salary of the states included in the chart above?*The following chart shows the number of packages a company sends out each month. Use the chart to answer the questions below. (Worth 2 questions)MonthPackages SoldJanuary555February341March301April278May178June192July223August256September343October405November501December632Find the mean number of packages sent out for the first 6 months of the year, then find the mean number of packages sent out for the second 6 months of the year. Compare these numbers to the overall mean number of packages sent out for the year. *Round to the nearest package.Calculate the mean number of packages sent out during summer. (May-August). *Round to the nearest package.Calculate the mean number of packages sent out during winter. (November-February). *Round to the nearest package.What percent increase in package shipment does this company experience during the winter as opposed to the summer? What could explain this? *Round to the nearest percent.In your chemistry class the grades are distributed a little differently than most classes. If you make the same grade as the average of the class you receive a C and then the grades are distributed for the rest of the class so that 20% of the class make an A, 25% make a B, 30% make a C, 15% make a D and the rest of the class fails. Answer the following questions based on this information. (Worth 2 questions)The grades on the latest chemistry test for the 8am class were the following: 74, 84, 55, 91, 56, 45, 88, 67, 78, 45, 93, 84, 75, 82, 74, 59, 90, 87, 75, 65The grades on the latest chemistry test for the 10am class were the following: 93, 80, 74, 69, 45, 92, 84, 75, 81, 77, 93, 59, 72, 86, 93, 90, 84, 74, 79, 57Based on the grade breakdown above, how many students in each class will receive a letter grade of an A, B, C, D and F?If you made an 84 on your chemistry test and you are currently in the 8am class, what grade would you receive? What about if you were in the 10 am class?If you made a 90 on your chemistry test, what grade would you have received in the 8am class? 10 am class? Do you think this kind of grading is fair? Why or why not?Name a time when it would be useful to know the mean, median and mode of a set of data. Measures of Dispersion WorksheetFor numbers1-3 below use the following scale for grades.The grades in a class on a recent test were: 80, 76, 81, 84, 79, 80, 90, 75, 75, and 80. What grade would a person earning a 76 get in this class? If the grades in a class are: 80, 65, 75, 82, 80, 78, 91, 74, 78, 94 and 85, how many people will receive an F? If the grades in a class on a recent assignment were: 65, 88, 92, 90, 87, 83, 77, 93, 86, 97, and 75. What grade would a person earning a 83 get in the class? Find the range, mean, and standard deviation for the following data set: 17 ,19 ,22 ,24 ,16 ,18 ,19 *Find the range, mean and standard deviation for the following data set: 23, 24, 45, 34, 83, 56, 45, 34, 54, 61 *Make a chart to show how to calculate standard deviation by hand given the following data set: 2, 1, 4, 3, 6, 3, 2, 4, 5, 3 *For a given month the mean daily closing stock price for Bank of America is $13.50 with a standard deviation of $0.32. For Wells Fargo stock the mean daily closing price was $49.75 with a standard deviation of $2.56. Which stock was more volatile? Find the mean and standard deviation for the following frequency distribution chart:*X (data point)Frequency8392130154162201Given the following data set find the mean, median, mode and range: 89, 72, 100, 97, 93, 97, 95, 86,78, 83 Explain an instance in the real world where it would be useful to know the mean and standard deviation of a set of data. Normal Distributions WorksheetAssume that a normal distribution has a mean of 12 and a standard deviation of 3. Using the 68-95-99.7 rule, find the percentage of values in the distribution between 6 and 15.From the percentage of area under a normal curve from z = 1.4 to z = 2.1Find the corresponding z score for a data point: x = 29 for a normal distribution given a mean of 24, a standard deviation of 8.Find the corresponding mean for a set of data containing the data point x = 5.6, standard deviation: 1.1 and z-score 0.9. If the average bag of skittles contains 98 skittles with a standard deviation of 12 skittles, what percent of skittles would you expect to contain more than 116 skittles? If the average grade on your English final was a 91 with a standard deviation of 6, what would be the cutoff grade to be in the bottom 30% of the class? If the average NBA player makes $2.5 million dollars a year with a standard deviation of $600,000 and there are about 446 players in the NBA, how many of the players would you expect to make more than $3.5 million dollars? *Round to the nearest player.The average score on the math section of the SAT was 518 with a standard deviation of 115 points the year you took the test, and you scored 555. What percentage of students taking the SAT in your year scored below you on the math section? A company is trying to figure out the optimal length of time for a warranty on their top rated vacuum cleaners. On average the top rated vacuum cleaner will run for 420 hours with a standard deviation of 15 hours. If the average person vacuums for 2 hours a week and the company wants no more than 5% of their top rated vacuums returned as defective, how long (in years) should the warranty be in order to guarantee this? *Round your answer to the nearest year.If 95% of all kids drink between 75 and 100 sodas a year, what percent of students would you expect to drink at least 86 sodas a year?Simple and Compound Interest WorksheetIf you invested $4,500 into an account paying 1.5% simple interest for 5 years, how much interest would you gain? How much money will be in your account at the end of the 5 years? If you made $500 after investing $10,000 for 3 years what percent simple interest did the account you invested in pay? * Solve the equation: 4x=12 *Samantha needs to pay off a late doctor’s bill of $3,500 which has been due for 5 months. If the interest on the bill is compounded monthly and the bill has an annual interest rate of 15% for being late, what will her total payment be on her doctor’s bill? If you are currently 25 and you plan to retire when you are 55 with $1,000,000 in your retirement account, how much will you have to set aside now in an investment account that compounds daily and pays 6% annual interest? In order to pay your car bill you borrowed $750 on one of your watches from the local pawn shop. If you agreed to pay the pawn shop $825 five months later to get your watch back, what simple interest rate is the pawn shop charging you on your watch?You are trying to go on vacation to Africa but you only have $1,500 and the trip is going to cost $2,500. If you invest your money into an account that pays 6.5% annual interest, compounded monthly, how long will it take you to have $2,500 to go on your vacation? *You purchased a living room set for your home for $4,000 and agreed to pay the set off in 36 monthly payments of $175 each. What will be the total sum of your payments?What will be the total amount of interest that you have paid?If you put $11,500 into an account that earned 1.2% annual interest, compounded monthly, and let the money sit for 5 years, how much money would you have at the end of the 5 year period? While going to college you borrowed a total of $23,000 which you must pay back. In one year what would be the difference in interest if your loans were compounded daily at 6% annual interest or if your loans were compounded daily at 8% annual interest?Loans and Credit Cards WorksheetIf you bought a sofa for $900 at 12% interest and agreed to pay it off over a 2 year period, how much would your monthly payment be?Tim wants to buy a new boat for $9,500. If the store is going to charge Tim 8% annual interest on his purchase (assume an add-on loan) answer the following questions. (worth 3 questions): Tim wants to pay the boat off in 3 years, how much will his monthly payment be?If Tim makes a down payment of $1,500, what will his new monthly payment be? If Tim wants his monthly payments to be $175, how much should his down payment be? For #3-4 use the unpaid balance method to compute the finance charge on the following credit card account. Last month’s balance: $475, payment: $250, interest rate: 13%, bought pair of boots: $110, returned a camera: $155.Last month’s balance: $685, payment: $75, interest rate: 12%, bought pet supplies: $75, bought groceries: $210, bought gas $100.For #5-6 use the average daily balance method to calculate the finance charge on the credit card account for the previous month. Month: August (31 days); previous month’s balance: $280; Interest rate: 18%DateTransactionAugust 5Made payment of $75August 15Bought a jacket for $135August 21Bought lunch for $16August 24Bought gas for $26 Month: April (30 days); previous month’s balance: $450; Interest rate: 15%DateTransactionApril 4Bought groceries for $125April 10Returned a shirt for $35April 16Bought home supplies for $190April 22Made payment of $50April 28Bought gas for $85Sarah went and bought a new couch set for $1,400. In order to pay for the couch set, Sarah took out a 2 year add- on loan from the bank with a 9.75% annual interest rate. How much will Sarah pay in interest over the 2 year period and how much will her monthly payment be? Explain the difference between the unpaid balance method and the average daily balance method when it comes to computing your credit card bill? Give an example where each method would be advantageous over the other. Annuities WorksheetGiven the information below in #1-3 find the value of the ordinary annuity after the given amount of time. Payment: $250; frequency of compounding: monthly; annual interest rate: 4%; length of time: 6 yearsPayment: $120; frequency of compounding: quarterly; annual interest rate: 3.5%; length of time:10 yearsPayment: $500; frequency of compounding: monthly; annual interest rate: 9%; length of time: 7.5 yearsHow much money would you have to pay each month to have collected $4,000 in a sinking fund in 5 years, given that the fund collects an annual interest rate of 3%?Kelly’s parents set up an ordinary annuity for her when she was born to help pay for her college tuition in 18 years. If they have put $100 a month into the annuity and it collects 4.5% annual interest, how much will be in the annuity when Kelly is ready to go to college? Sarah wants to save $15,000 in 12 years for a down payment on a house. If her annuity pays 0.9% monthly interest, how much will Sarah’s monthly payment be? Solve the following for X: 5x=20 *You have decided to retire once you save $1,000,000. If you put $200 a month into an ordinary annuity that pays an annual interest rate of 8%, how long will it take until you are able to retire? *Round to the nearest year?How many years will it take you to save $20,000 in an ordinary annuity if you save $150 a month and your annuity pays 4% annual interest? *Round to the nearest year?If you make quarterly payments of $400 into an ordinary annuity that pays 6% interest, how much will your annuity be worth after 18 years?Lab #1To earn credit you need to show all your work. Please remember you have 1 week to complete the lab, otherwise there will be points deducted.Situation #1: Bell UniversityThere is a hypothetical university called Bell University in New York City. At Bell University there are a total of 25,435 students, in which 56% of the total student body population are females and 44% of the student body population are males. Bell University is very expensive and 19,890 students are on financial aid, while 2,145 students are not on financial aid but have been given scholarships because they were very smart; leaving the rest of the students to pay the full cost of tuition. The cost of Bell University is $43,850 a year, with 25% of this cost coming from housing costs, 12% from meal plan expenses, 4% book costs and 36.75% tuition fees. As you can see Bell University is quite a unique place, but not as unique as the degrees that are offered there. At Bell University 58% of the female student body population takes classes in cooking while 63% of the male student body population takes classes in wood-working. But again it is not that simple. Out of the students who take cooking, 34% have a concentration in baking, 42% have a concentration in decoration and design, and the other cooking students have no clue what their concentration will be. And you think that is bad? The wood-working students have it just as bad. Within the wood-working department there are 150 faculty members, 112 of whom are male, while the rest are female. Out of the male staff members, 68% have a Ph.D, while 73% of the female staff members in the wood-working department have their Ph.D. So as you can see Bell University is quite a diverse place, between the cost of attending the school, to the student body population and even the courses offered, it sounds like quite the place. Answer the following questions about Bell University: * Round all people to the nearest person at each calculation and round all dollar values to the appropriate place. Don’t assume you know anything about Bell University other than what is given above. How many students at Bell University take cooking classes and have a concentration in baking? How much of the total cost to attend Bell University (in $) is not from one of the specific sources listed above? (aka not from books, meal plan, etc.)How many female staff members in the Wood-Working department don’t have a Ph.D?What is 60% of the total meal plan cost?What percent of the female students take cooking classes but have no clue what their concentration will be in?Write a ratio for the number of students taking wood-working to the total number of students enrolled at Bell University. Write the ratio in lowest form. What percent of the total student body population has to pay full tuition? *Round your answer to the nearest whole percent.If 15.5% of the students on financial aid get 75% of the cost of attendance covered, how much does this cost the school each year?Situation #2: ShoppingAs usual, it is a typical summer afternoon and you decide to go shopping. But not just anywhere, you decide to go to the mall of course, where there will be plenty of deals to choose from. While at the mall you encounter the following deals: At Macy’s they will give you 25% off your total purchase (up to $50 off). At J.C. Penny you can get $11 off for each item that you buy.At Dillard’s you will receive 5% off your first item, 10% off your second item, 15% off your third item and so on. (The items are first ranked from most expensive to least expensive).At Belk’s they will give you $15 off $50 or $40 off $100 (you can’t combine these offers).If you want to buy the following 4 items, where would be the cheapest place to buy them (given the sales above)? Then figure out how much it will cost you to buy all the items at the cheapest store with 6.75% sales tax. Remember to round your cost to the appropriate place. Items to buy: A pair of pants: $25, a t-shirt $15, a new dress $64, and a hat $23.Situation #3For every 4 people in the world that like cheese pizza, 5 like pepperoni. If there are 1400 students in Math 110 that like cheese pizza, how many will like pepperoni? Another study found that 2 out of 3 pepperoni pizza lovers like thick crust rather than thin crust. Out of the students in Math 110 who liked pepperoni pizza, how many are thick crust lovers? But that’s not it…Out of all of those thick crust, pepperoni pizza lovers can you believe that 7 out of 8 of them would rather have their pizza delivered than from the grocery store? And last but not least, 4 out of 6 of the people who are pepperoni, thick crust, delivery loving people, would like that pizza to be delivered from Dominos. So if I am going to throw a party for all the students in Math 110, how many people would prefer to have pepperoni, thick crust pizza delivered from Dominos? Round to the nearest person as you go along and make your calculations. Also what percent of the total number of students in Math 110 like pepperoni, thick crust pizza delivered from Dominos? Round to the nearest percent.Situation #4Sadly last week you found out that your great-grandma passed away, but what you didn’t know was that your great-grandmother was secretly a very rich woman. Upon the opening of her will you see the following specifications on how her money is to be distributed. Answer the following questions based on your great-grandmothers money. Your grandmother was worth 1.275 million dollars. She wanted 80% of the money to be split evenly between her 5 kids. She wanted 20% of the left over money (after being given to the kids) to go to her local church. She wanted 20% of the money given to the church to go to the children’s program. She wanted 35% of the money not given to the kids to go toward a vacation for her best friends: Ruth and Anne Marie. She wanted $5,500 to be left to her dog Fluffy. She wanted all the left over money (after all of the following above has been distributed) to go into a college fund for her grandkids. How much money will the following people get: Each of her 5 kids, the church (not including the children’s program), the children’s program at the church, Ruth and Anne Marie respectively, and the college fund for her grandkids? LAB #2Please complete the entire lab. In order to get any partial credit you will have to show your work. Round all money values to the appropriate place. Don’t round any of your answers (except $) unless it says so in the question.Situation #1: Grandma’s HouseLast week I decided to go visit my grandma. It took me 16,200 seconds to get to my grandma’s house going 8,851,392 cm/hour. Once there, my grandma told me she wanted to do a fun activity together, so we decided to bake cookies. Chocolate chip, my favorite! The recipe called for the following ingredients: 2 cups of flour, 34 cup chocolate chips,1 12 cups butter, 2 teaspoons vanilla, 3 eggs, 14 cup brown sugar and 13 cup white sugar. And boy were the cookies good! The recipe made a whole 2 dozen cookies.How long did it take you to get to Grandma’s house in hours? How fast were you going in miles per hour? How many miles did you drive to get to Grandma’s House?Excluding the vanilla and eggs, how many cups of ingredients’ were included in the chocolate chip cookie recipe? Write your answer as a mixed number.If it cost $15.85 to buy all the ingredients for the chocolate chip cookie recipe, how much did the ingredients cost per cup? (Again excluding the vanilla and eggs).What was the average cost per cookie?Situation #2: Real world situationsYou work for a restaurant and they put you in charge of ordering the beef from the retailer each week. If you need to make 150 hamburgers each day and each hamburger patty weighs 6 ounces before cooking, how many pounds of beef do you need to order from the retailer for the week? * Round to the nearest pound.If a paper clip weighs 1 gram, how many paper clips will you get in a 0.8 kilogram box of paper clips?You are traveling down the highway and notice mile markers and reflectors as you go along. If there are 11 reflectors between the mile markers and the reflectors are evenly spaced, how many feet are between each reflector?To get power to an air compressor 55 feet of extension cord is needed, but at a job site only a 14-meter extension cord is available. Will there be enough extension cord to power the air compressor? **Though this is a yes or no question, no credit will be given for this answer without supporting work.Your best friend lives 700 miles away and you told her you would meet her tonight at her house. If you are traveling at 0.03 km/sec will you make it to your friend’s house in 8 hours? If you had 1 meter of yarn , your brother has 6 yards of yarn, your sister has 23 feet of yarn, your mom has 132 cm of yarn and your dad has 58 inches of yarn, how much yarn (in cm) does your family have combined?When skydiving they have a 87 kg weight limit. If you weigh 140 lbs and your equipment weighs 50 lbs, can you go skydiving? **Though this is a yes or no question, no credit will be given for this answer without supporting work.Situation #3: Buying a vehicleA customer buying a new car has narrowed her decision down to two finalists: a hybrid selling for $32,000 and an economical non-hybrid selling for $22,000. The average fuel economy of the hybrid is 48 mi/gal, compared to 30 mi/gal for the non-hybrid. By purchasing the hybrid, the customer will receive a one-time tax credit of $1,500 and will save about $500 over the life of the vehicle on discounted auto insurance. Assume that the customer will keep each car for 120,000 miles and that the cost of fuel will average $3.80 per gallon over that time period. What will be the total cost of fuel for the non-hybrid car for 120,000 miles?What is the total cost of fuel for the hybrid car for 120,000 miles?Find the total cost of the non-hybrid car, everything considered, for 120,000 miles.Find the total cost of the hybrid car, everything considered, for 120,000 miles. If the total cost were the only consideration, which vehicle would the customer choose?Situation #4: Home RepairsFall is that time of the year in the Phillips’ household where everything seems to start breaking down. First it’s the washing machine, then the vacuum and now the sewer is backed up. The Phillips’ wonder if they will ever get a break, but for now they must repair what is broken and figure out the cost to do so. Washing machine problems: The Phillips’ washing machine used to run fine but now it is flooding every time you try to wash your clothes. In a normal load of laundry the washing machine uses 25 gallons of water per hour but the Phillips’ washing machine is now outputting 14 cup of water per second. Vacuum: The Phillips’ vacuum used to cover 10 square feet per second, but now it only covers 3 square yards per minute, so they’re thinking they need to buy a new vacuum.Sewer problems: The 0.82 miles of sewer system in the Phillips’ yard is backed up. The sewer system processes 10 gallons of water per yard, so you can just imagine the back-up in their yard. The repair man said that the whole line is going to have to be replaced which costs $0.15 per foot. Questions about the repairs.How many more gallons of water per hour is the washing machine putting out now that it is broken?If water cost $0.08 a cup, how much more are you paying for water (every hour) now that your washing machine is broken?How many gallons of water does your sewer system process over the whole length of the yard? How many cups is this?How much is it going to cost to replace the whole sewer system?How many less square feet per minute does your vacuum now cover that it is broken?LAB #3Please read each question carefully. No credit will be given for a wrong question without appropriate work, so please show ALL work. Do not round any values unless it says so in the question. Remember to include units in your answer and throughout your work. For pi use 3.14.Situation #1: Crossword PuzzleFill in the following crossword puzzle with the appropriate vocabulary word: Across1. Four-sided polygon.3. Type of triangle where none of the side lengths are the same.4. Half the diameter.6. 6-sided polygon.7. Measured in cubic units.9. Name of the theorem used to find the length of a side of a right triangle.12. Half a circle.13. Type of triangle where at least 2 of the sides are equal in length.15. The area between 2 concentric circles.16. Distance around the outside of a figure.17. 5-sided polygon.18. Type of triangle where all 3 sides are equal in length.19. Angle measuring less than 90 degrees.Down2. A line that cuts through a pair of parallel lines.5. Twice the length of the radius.8. Distance around a circle.9. Opposite sides are parallel and equal in length.10. The number of square units of surface within a figure.11. Angle measuring exactly 90 degrees.14. Contains 2 parallel sides and 2 non-parallel sides.Situation #2: Backyard PlanningYou just moved to a new city and bought a brand new house. The plus side of your new house is your beautiful, big backyard. In your backyard you want to have the following: a swimming pool, a play area for your kids, a fence for your dog and a patio so that you can entertain your friends. The features in your backyard have the following dimensions: Your whole yard is 4840 yards by 2420 yards, but 9,565,250 square yards of this is woods. You want the area of your pool to be 314 meters2, and you would love to have a play area for your kids that is 33 feet by 48 feet. As far as a patio for your house, you would like it in the shape of a rectangle with the patio having a total perimeter of 68 feet with the length being 6 yards. Last but not least you are going to plant grass in your backyard everywhere, where the pool, play area, woods and patio are not located so that your dog has somewhere to play.Given all the information about your backyard answer the following:What is the area of your pool, kids play area and patio in square feet?** Round each to the nearest square foot.How much grass in square feet do you need to plant in your yard?If grass seed cost $11 a bag and a bag covers 3,300 square feet, how many bags of grass seed do you need to cover the whole yard, and how much will it cost you for grass seed? *Round up to the nearest bag of grass seed. How many feet of fencing do you need for your yard, if the whole yard (including the wooded area) is going to be surrounded by fencing. Explain how you got your answer. Situation #3Go home and find an object around your house, this object needs to be a 3D object (Ex: you can’t choose a piece of paper). Record what object you have chosen and the dimensions of each face of the object. After you have recorded the object and the dimensions of each face, calculate the area of each face of the object and the volume of the object as a whole. **Be especially careful to include units for everything in this question so that I can get a sense of the size of the object you have chosen. Situation #4: Perimeter and AreaFind the perimeter and area of the following shapes. Make sure to show all work and include correct units. **Round the area and perimeter to the nearest tenth. (Round only your final answer). Figures are not always drawn to scale. Situation #5: Volume and Surface AreaFind the volume and surface area of each object, make sure to show all work and include correct units. **Round the volume and surface area to the nearest tenth. (Round only your final answer). When determining surface area imagine that you can pick up the figures below. Figures are not always drawn to scale. 16 ‘’12 ‘’16 ‘’12 ‘’Half a sphere with a radius of 8 feet. In the picture above the height of the cylinder is 13 inches and the diameter of the semicircle is 12 inches.Situation #6: AnglesFind the angle measurement of all the missing angles denoted by letters in each figure. Assume all numbers in the given figures are angle measurements. Figures are not necessarily drawn to scale. LAB #4The purpose of this project is for you to get real life experience working with graphs and data. Pick one of the following situations below to complete for your lab. Situation #1: Making a Budget (2 graphs, 2 pages)For this situation you need to make a monthly budget. Consider the following when making your budget: How much do you spend on food? Bills? Investments? Car payments? Medical Bills? Cell Phone? Etc. The budget should be thorough to the best of your ability. Then you need to create a graph that displays your monthly budget and write up a 1 page report that talks about your savings habits. Looking at your budget you made, can your spending habits be improved? Is there a benefit to saving money? What category would you have to decrease in order to save more money? Etc. Then I want to you research different savings and retirement options and in a 1 page report talk about your findings, while using a figure to display the information that you discuss in your paper. You could compare different options such as a 401K or a Roth IRA, you can talk about mutual funds etc. It is up to you, just be thorough, and explain the concept as if I have no clue what you are talking about.Situation #2: Buying a Car (1 graph and Stand. Dev/Mean and 2 pages)In this situation you will have to pretend that you are buying a car. In doing so you are going to have to research different makes and models of cars and think about the following: What all goes into buying a car? What kind of car will you buy and how much is it going to cost you? Do you want an environmentally friendly car or not? Etc. For this situation you will need to research 5 different non-new cars, then create a graph comparing at least one feature of the 5 cars (can’t be price). You can compare their speed, number of seats etc. Then in a 1 page report tell me (based on your graph) which car you would chose and why? Then I want you to research 5 new cars on the market and I want you to look at the price of the vehicles. Considering the prices of the 5 new cars I want you to calculate the mean and standard deviation of the purchase prices (showing what you do by-hand), and write a 1 page report summarizing your findings. From this list of 5 new vehicles which one would you chose and why? How much did the price vary between the cars? Was the purchase price the only factor in your decision etc. Please be thorough and explain as if I had no clue what you are talking about. Situation #3: Buying Stocks (2 graphs, 2 pages)**Please do NOT pick this situation if you have NO knowledge of the stock market and you are not willing to come and see me to learn. For this situation you will have $5,000 to invest. Invest all the money (to the nearest whole number of shares) into a single stock and watch that stock for 4 days. Record the stock you chose, the value of the stock for all 4 days, and the value of your investment for 4 days and make a graph displaying the change in your investment value. Then in a 1 page report tell me about how you chose your stock and how you calculated your investment value over the 4 day period. If you had to do it over again if you would have chosen the same stock etc. Then research the stock market a little bit and tell me about an event that occurred in the stock market in a 1 page report while using a figure to display information that you discuss in your paper. You can talk about the dips in the market, a company’s stock splits, or a company’s dividend payouts etc. The choice is up to you, but you need to explain it as if I have no clue what you are talking about. Be thorough. LAB #5Situation #1: Student LoansShow ALL your work for this situation, even writing down what you put into your calculator. The majority of your points will come from your work and your explanation (#3), not your answers.For this situation you are going to calculate how much interest you will have to pay on school loans given a set of situations. Do not round your calculations till the end. Loans you took out to complete your undergraduate degree: 2010-2011: Direct Subsidized Loan$3,2502011-2012: Direct Subsidized Loan $4,1002012-2013: Direct Subsidized Loan $7002012-2013: Direct Unsubsidized Loan $2,0002012-2013: Direct Subsidized Loan $2,7502013-2014: Direct Subsidized Loan $5,000Assume the following: Your unsubsidized loan starts collecting interest the day you take it out. You take out the unsubsidized loan on August 1st, 2012 and you graduate on May 1st in 2014. Your subsidized loans collect interest the day you graduate, but the first payment for all the loans above is not due until 6 months after you graduate, on November 1st, 2014. Also assume that the interest for all the loans above compounds daily. You can forget about leap year.Given all this information answer the following: On the first day that a payment is due: November 1st, 2014 how much interest do you owe above your initial principal? (aka how much interest have your loans collected up to this point….before your first bill is even due?)2nd question: If the unsubsidized loan was $5,000 how much would this have changed your total interest due in question #1? **Note your principal is different in this question. 3rd question: If you wanted to pay off your loans in monthly payments starting on November 1st 2014, would calculating your monthly payment be as simple as taking your total in question #1 (principle + interest) and dividing by the number of months you want to pay off your loan in? Example: If I wanted to pay the total amount of my loans off in 5 months, to determine my monthly payment could I do: Total ÷ 5 months = monthly paymentSituation #2: Credit Card BillsShow all work, even the work you put into the calculator. The majority of points given will be for your work, not for the answer. Assume you open a credit card at the beginning of the year: January 1st, with an opening balance of $0.00. The annual interest rate on the card is 18%, and your bill is due each month. Starting in January the following charges and credits occur on your account: DateCreditChargeJanuary 5$45- GasJanuary 9$115-ClothesJanuary 13$85-GroceriesJanuary 14$65-Return clothesJanuary 18$11-Lunch January 25$32-GasJanuary 27$127-BootsJanuary 29$200-PaymentFebruary 2$38-GasFebruary 6$58-GroceriesFebruary 9$199- Car InsuranceFebruary 14$75-B day MoneyFebruary 17$28-GasFebruary 22$6-LunchFebruary 23$35-Dinner & MovieFebruary 26$78-GroceriesFebruary 28$150-PaymentCompare what your Finance Charge will be for the month of March using the Average Daily Balance Method and the Unpaid Balance Method. Assume the year is not leap year. * Also assume the only things you charged/paid are listed above. Study ReferencesMath 110 Formula SheetAreaPerimeterCircle: πr2Circumference: πD or 2πrRectangle: length*widthRectangle: 2*length+2*width Square: side*sideSquare: 4*sideParallelogram: base*heightParallelogram: Add all the sidesTriangle: 12*base*heightTriangle: Add 2 sides and hypotenuseArea FormulasVolume FormulasSurface Area FormulasTrapezoid: (b1+b2)2*hRectangular Solid: l*w*hRectangular Solid: 2lw+2lh+2whArea of an Isosceles Triangle:12ba2-b22Right Circular Cylinder: πr2hRight Circular Cylinder: 2πrh+2πr2Hero’s Formula:ss-as-b(s-c) where S = a+b+c2Right Circular Cone:13πr2h Right Circular Cone: πrr2+h2Area of a Regular Hexagon:3a232≈ 2.598a2Sphere:43πr3Sphere: 4πr2Area of an Equilateral Triangle: a234≈0.433a2Pythagorean Theorem:a2+b2=c2Other Useful FormulasSimple Interest: I = PRTStandard Deviation of a Sample: S= (x-x)2n-1Regular Hexagon: d=2a and a=0.5dStandard Deviation of a Population : σ=(x-?)2nRegular Hexagon: f~1.732a and a~0.577fCoefficient of Variation: CV=Sx*100%Annuities: A=R1+rNN*T-1rNZ-Score: z=x-μσCompound Interest: A = P1+rNN*TAdditional Finance Formula SheetConversionsLength12 inches1 foot3 feet1 yard5,280 feet1 mileCapacity8 fluid ounces 1 cup (c)2 cups1 pint (pt)2 pints1 quart (qt)4 quarts1 gallon (gal)Time60 seconds1 minute60 minutes1 hour24 hours1 day7 days1 weekWeight16 ounces1 pound (lb)2,000 pounds1 tonU.S. –Metric1 inch2.54 cm1 foot~ 0.30m 1 yard (yd)~0.91 m1 mile~1.61 km1 cup~236.59 ml1 quart~0.95L1 gallon~3.79 L1 ounce~28.35g1 pound (lb)~0.45kgMetric Conversions: King Henry Died Monday Drinking Chocolate Milk or KHDMDCMThis is used for conversions dealing with Weight (Mass): grams, Capacity (liters) and Distance (meters)Z-ScorePercentile0.050-2.70.350.153.98-2.6.470.257.93-2.5.620.361.79-2.4.820.465.54-2.31.070.569.15-2.21.390.672.57-2.11.790.775.8-2.02.280.878.81-1.92.870.981.59-1.83.591.084.13-1.74.461.186.43-1.65.481.288.49-1.56.681.390.32-1.48.081.491.92-1.39.681.593.32-1.211.511.694.52-1.113.571.795.54-1.015.871.896.41-0.918.411.997.13-0.821.192.097.73-0.724.22.198.21-0.627.432.298.61-0.530.852.398.93-0.434.462.499.18-0.338.212.599.38-0.242.022.699.53-0.146.022.799.65Equations WorksheetUseful information for equations: Sales Tax Formula: Tax = Tax Rate*Item Price** For this formula you need to change the tax rate (%) into a decimal.Example: Calculate the tax if you had to pay 9% tax on $50 worth of food. Tax = (0.09)*($50) = $4.50The total price for the food would be: Item Price + Tax = Total Cost Ex: Total Price = $4.50 +$50 = $54.50Commission Formula: Amount of Commission = Rate of Commission *Amount of Sales**For this formula you need to change the commission rate (%) into a decimal. Example: If you earn 8% commission for every apartment you sold and you sold $23,851 worth of apartments how much commission will you make?Commission= (0.08)*($23,851) = $1,908.08You would make $1,908.08 in commission. Find a sale price formula: Amount of Discount = Rate of discount * Original priceSale Price = Original Price – Amount of Discount**For this formula you need to change the rate of discount (%) into a decimal.Example: If a pair of jeans for $42 was on sale for 15% off the price, how much would you have to pay for the jeans?Amount of Discount = (0.15)*($42) = $6.30 (this is the amount you get off the original price)Sale Price = $42 - $6.30 = $35.70 Thus you will now pay $35.70 for the jeans after the discount. Find the Percent Increase or Percent Decrease Formula: amount of increase or decreaseoriginal amount=percent increase or decrease (leave as %)100*This formula you will use the % (because it is already over 100), do NOT change it to a decimal.Ex: In 1990 a town had a population of 3,000. In 2010 its population had grown to 6,600. What was the percent increase in the population over the 20 year period?Amount of Increase = 6,600 people – 3,000 people = 3,600 peopleOriginal Amount = 3,000 people3,600 people3,000 people=x100Solve the proportion by cross multiplying: (3,600*100) = (x*3,000)360,000 = 3,000x Then divide each side by 3,000 and x = 120 So the town had a 120% increase in population over the 20 year period. Simple Interest Formula: I = P*R*T or interest = principal *rate*timeEx: How much interest would you get if you invested $2,000 at 10% interest for 4 years?I = (2,000)*(0.10)*(4) = $800You would get $800 interest. Compound Interest Problems:A=P1+Rnn*TA = Amount in account after T yearsP = principalR = Interest Rate in Decimal Formn = # of times the interest is compounded annuallyT = time (years)Ex: How much money would you have in your account if you invested $3,000 for 2 years compounded annually at 5% interest?A = 3,0001+.0511*2=3,000(1.05)2 = $3,307.50So $3,307.50 would now be in your account. Remember annually n = 1, semiannually n =2, quarterly n=4, monthly n =12Weekly n = 52 and daily n = 365Review #1**Round all answers (if necessary) to the nearest tenth. Use 3.14 for pi.This is your first set of final review questions. This list is NOT complete, but it is meant to get you thinking about what you know and what you need a review of. Beginning of class to mid-term: If your dog eats 9 pounds of dog food a week, how many pounds of dog food will he eat in 20 days?Convert the following to a percent:3.50.630.0032Convert the following to a decimal: 73%215%2%Convert the following to a fraction in lowest terms: 34%0.25What is 65% of 420?86% of what number is 43?What percent of 120 is 45?If you bought a pair of pants for $75 and the pants were 15% off, but you had to pay 7% sales tax, how much total did you pay for the pants? (aka what will the cashier charge you?)If you earn 11% commission on all the apartments you sell, how much will you make if you sell $45,000 worth of apartments?Convert the following: 20 cu ft to cu in3 miles to feet11 yards to inches132 lbs to kg (2.2 lbs~ 1 kg)50 mg to grains (60 mg ~ 1 gr)A triangle contains a right angle and an angle measuring 32 degrees. Find the missing angle in the triangle. If Angle A is a vertical angle to Angle B and Angle A is 94 degrees, what is the measure of Angle B?Find the probability of rolling a 4 when rolling a six-sided dice. Convert 25°C to FahrenheitFor more study questions on angles refer to Lab #3, on the last page where you had to find the missing angles.Second half of class. Find the area and perimeter of a square that has a side length of 15 feet. Find the area of a triangle that has a base of 11inches and a height of 6 inches.Find the hypotenuse of a right triangle if the legs measured 5 feet and 12 feet. Find the missing side length of a right triangle if the hypotenuse measures 25 yards and one leg measures 24 yards. Find the area of a triangle that has a base of 10 feet and a side length of 6 feet. Do not round calculations, only round your final answer to the nearest tenth.Find the area of a hexagon with a side length a = 8 feet. Find the area of a ring if the outside diameter of the circle is 8 inches and the inside diameter is 6.5 inches.Find the surface are and volume of the following shapes: A cylinder with a height of 4 cm and a radius of 2 cm. A cone with a height = 10 ft and a radius = 6 ft.c. Rectangular prism with a height of 4 ft, a width of 6ft and a length of 8 ft. You should know how to read a basic graph, this includes line, bar and pie graphs. You should also know when to use each graph aka: line graph (time), bar graph (comparing quantities) and pie graph (comparing parts of a whole).Find the mean (round to the nearest tenth), median and mode of the following set of data: 9,12, 13,9,11,13,8How much greater is the median than the mean?What is the name for the mode?Find the range, mean and standard deviation for the following sample set: 18,3,8,7,7,9,13,7Find the raw score of a set of data if the mean is 60, the standard deviation is 5 and the z score is 0.84Using the 68-95-99.7 rule if the mean of a set of data is 15 and the standard deviation is 3, give the percent of values you would expect to find: Below 12?Between 12 and 18?Above 21?For a marathon race the average finishing time is 245 minutes with a standard deviation of 20 minutes. For this particular race, what is the cutoff time for a runner to finish in the top 20%? Review #2Find the interest earned in an account if you invested $3,000 at 8% interest for 18 months. How much money would you have in your account if you invested $2,500 compounded quarterly at 6% interest for 3 years?How long would it take your investment to double if you invested $10,000 at 10% interest compounded monthly for 4 years?Using the add-on Interest Method how much would you pay each month for a couch you bought for $2,000 at 6.5% interest, if you have 6 months to pay the couch off? Use the unpaid balance method to find the finance charge on the credit card account described below: Your last month’s balance was $415; you made a payment of $150, your interest rate is 18%, and this month you bought new shoes for $95 and groceries for $225. Use the unpaid balance method to find the finance charge on the credit card account described below: Last month’s balance: $780; you made a payment of $214, Your credit card interest rate is 17.5%, and this month you bought a new shirt for $35, a chest for $156, returned a pair of boots for $130 and bought some gas for $55. Use the average daily method for #7-8 to compute the finance charge that will appear on your credit card statement for the months below. Month: July (31 days): Previous Month’s Balance: $175. Annual interest rate: 15%DateTransactionJuly 5Made Payment of $86July 11Charged $125 for groceriesJuly 18Charged $36 for dinnerJuly 26Charged $121 for new t-shirt and jeansGiven a 21% annual interest rate for the Month of October (31 days): Previous month’s balance: $215DatePaymentOctober 7Charged $35 for gasOctober 14Charged $78 for art suppliesOctober 20Made a payment of $110 October 24Charged $13 for lunchAssume you wish to save $2,000 in a sinking fund in 3 years. The account pays 8% interest compounded quarterly and you will also make payments quarterly. What should your quarterly payment be?You want to set up an ordinary annuity so that you will have some money for retirement. If you are 35 years old now and plan to retire at the age of 55, how much will you have in your annuity if, starting now, you make monthly payments of $250 into an annuity that pays an annual interest rate of 7.5%? Sarah wants to put away some money for a vacation. If Sarah puts $150 every month into an ordinary annuity that pays 9% interest, how much will Sarah have saved for her vacation after 3 years? Find the mean, median, mode and standard deviation of the following sample of ages at a Justin Bieber Concert: 15,14,13,17,17,21,15,16,18,21,22,45,58,12,11,19,18,17,21Can you tell anything from this Bieber data?What are the symbol differences for the standard deviation of a population and of a sample?If you have a normal distribution, what percent of the data lies below the mean?Find the area between the following Z-scores: 1.38 and 2.48Find the raw score for a set of data if the mean is 33, the standard deviation is 2.2 and the z score is 1.32.Find the hypotenuse of a triangle if the two side lengths are 28 and 45.At Home Depot a rubber door mat that is 3.5ft by 4.25 ft cost $32, while a similar carpet door mat at Lowes that is 5ft by 4.75 ft costs $55. Which mat is cheaper per square foot? Find the area of an equilateral triangle with a side length of 22 cm.Work on finding the area of irregular figures. Good examples were in Lab #3.Review #3A few hints for the exam: know what formula’s you actually need and which ones you don’t (and what formula’s are used for what). Also know how to work a calculator, especially for problems dealing with compound interest and annuities and know how to round properly. To pay for a down payment on his new home, Sam wants to save $9,000 in 6 years by making monthly payments into an ordinary annuity. If the annuity pays 0.8% monthly interest, what will Sam’s monthly payment be? If you put $375 a month into an ordinary annuity that paid 4.5% annual interest for 36 months what would be the value of your annuity at the end of the 3 year period? Solve the following equation for the variable X: 25X = 275What percent of 16 is 7? Convert 89°F to Celsius*Find the probability of randomly picking a Spade out of a standard deck of cards. At Belk’s in the mall a North Face jacket is $185 but at TJ Maxx the same jacket will cost you $105. What percent discount would you be receiving if you bought the jacket at TJ Maxx instead of at Belk’s? *Convert 123 square yards to square feet.Find the probability of picking a ten of Spades and then without replacement a Heart from a standard deck of cards.Convert 2500 ft/min to in/sec.Convert 12.5 km/hr to cm/sec. *Round your answer to the nearest tenth.Find the missing angles:Find the area of an equilateral triangle with a side length of 8 meters. Round your answer to the nearest tenth. Find the side length of a square with an area of 49 yards squared.Find the hypotenuse of a triangle with side lengths of 9 cm and 12cm. Find the area of an annulus if the diameter of the largest circle is 10 feet and the diameter of the smaller circle is 7 feet. Round your answer to the nearest tenth. Use 3.14 for pi. Find the volume of a cylinder with a radius of 3 yards and a height of 5 yards. Round your answer to the nearest tenth. Use 3.14 for pi. Practice reading graphs.Calculate the mean (round to the nearest tenth), median, range and mode of the following set of data (ages of children at the mall): 15,14, 16,17,14,18, 19, 21, 18,16,17,15,16,16Find the standard deviation of the sample in #17. (Round to the nearest tenth)A company is trying to figure out the optimal length of time for a warranty on their top rated vacuum cleaners. On average the top rated vacuum cleaner will run for 420 hours with a standard deviation of 15 hours. If the average person vacuums for 2 hours a week and the company wants no more than 5% of their top rated vacuums returned as defective, how long (in years) should the warranty be in order to guarantee this? *Round your answer to the nearest year.If the average NBA player makes $2.5 million dollars a year with a standard deviation of $600,000 and there are about 446 players in the NBA, how many of the players would you expect to make more than $3.5 million dollars? *Round to the nearest player.Remember to review questions for annuities, credit cards and loans.Select ExamplesPercents:Writing a percent as a decimal or fractionTo write a percent as a fraction, write the percent as a fraction of 100.Example: ?Write 23% as a fraction. ????23% = Example: ?Write 50% as a fraction. ????50% = To write a decimal as a percent, look to see how many hundredths you haveExample: ?Write 0.4 as a percent. ???0.4 = 0.40 = = 40%You may notice this is the same as moving the decimal place to the right two placesExample: ?Write 0.057 as a percent. ??Moving the decimal to the right two places: ?5.7%To convert a percent to a decimal, write the decimal out of 100 and divide. ?Notice this is the same as moving the decimal place to the left two places.Example: ?Write 12.5% as a decimal and as a fraction. ??As a decimal, 12.5% = To write as a fraction, we could start with the decimal: ?To write a fraction as a percent, first divide to find a decimal, then write it as a percent.Example: ?Write as a percent. ? = 40%To find the percent of a wholeOften we want to find the percent of a whole. ?To do this we multiply, first writing the percent as a decimal:whole · percent = partExample: ?Find 20% of 80. ??80 is the whole. ?To find 20% of it, we convert 20% = 0.20 and multiply:. ?20% of 80 is 16.Example: ?If sales tax is 9.6%, find the sales tax on a $200 purchase.We would multiply: ?. ?Tax would be $19.20.Solving Percent Problems:Pieces of a percent problemPercent problems involve three quantities: ?the base amount (the whole), the percent, and the amount (a part of the whole). ??The amount is a percent of the base.Example: ?50% of 20 is 10. ??20 is the base (the whole). ??50% is the percent, and 10 is the amount (part of the whole)In percent problems, one of these quantities will be unknown. ?Here are the three cases:Example: ?What is 25% of 80? ??80 is the base (the whole) we are finding a percent of. ?The percent is 25%. ?The amount is unknown.Example: ?60 is 40% of what number? ??The percent is 40%. ?The unknown is the base that we are finding a percent of. ?The amount (part of the whole) is 60.base · 0.4 = 60??? ??? To solve for the base, we divide both sides by 0.4??? ??? 60 is 40% of 150.Example: ?What percent of 320 is 80? ??The base we are finding a percent of is 320. ?The percent is unknown. ?The amount is 80.Solving percent problemsTo solve percent problems we use this relationship: base*percent=amountRates and Ratios: Ratios are used to compare amounts or describe a relationship between two quantities, usually of the same type.Example: ?Out of 300 students in the class, 175 are female. ?Express this as a ratio.The ratio of female students to total students is . ?This is often read “175 out of 300”. ?In this case, this ratio could be expressed in lower terms as . ?Sometimes you’ll see this written as “7 to 12” or “7:12”Example: ?A rectangle is 14 inches long and 8 inches wide. ?What is the ratio of length to width?The ratio is A rate is a ratio that compares quantities with different units. ?Examples include miles per hour, miles per gallon, dollars per hour, cost per ounce, etc. ??As with ratios, we usually reduce rates to lowest terms.Example: ?Write the rate as a simplified fraction: ??6 teachers for 63 students.Example: ?Write the rate as a simplified fraction: ??With 5 gallons of gas you drive 150 milesA unit rate is a rate where the denominator is 1. ?To accomplish this, we may end up with a fraction or decimal in the numerator.Example: ?A 24 ounce bottle of shampoo sells for $3.60. ??Find the unit rate (unit cost: cost per ounce)We would typically read this unit rate as “15 cents per ounce”Example: ?Kate worked 32 hours last week and earned $304. ?Find her unit pay rate (dollars per hour).We are looking for dollars per hour, so dollars must go in the numerator, and hours in the denominator.Kate earns $9.50 per hour.Proportions:A proportion is an equation showing the equivalence of two ratios or rates. ?Example: ?Is this proportion true? Yes, this proportion is true since the two fractions are equivalent since , and both rates have the same units of “cups flour per cookies.” Solving proportionsIf a proportion is true, then if we cross-multiply, both sides will be equal.Example: ? is a true proportion since ??? To solve for an unknown in a proportion, we can cross-multiply, then divide.Example: ?Solve for the unknown n. ?Cross multiplying, , or . ?Dividing, . ?Probability:Given that all outcomes are equally likely, we can compute the probability of an event E using this formula:The result of an experiment is called an outcome. An event is any particular outcome or group of outcomes. A simple event is an event that cannot be broken down furtherThe sample space is the set of all possible simple events. Example (Basic Probability and Rolling Dice Part 2)If we roll a 6-sided die, what’s the chance of:a) P(rolling a 3)b) P(rolling a number bigger than 4)Solution:The sample space is {1,2,3,4,5,6}a) There is one outcome corresponding to “rolling a 3”, so the probability is b) There are two outcomes bigger than a 4, so the probability is Example (Basic Probability and Drawing from a Bag)Let's say you have a bag with 20 cherries, 14 sweet and 6 sour. If you pick a cherry at random, what is the probability that it will be sweet? Solution:There are 20 possible cherries that could be picked, so the number of possible outcomes is 20. Of these 20 possible outcomes, 14 are favorable (sweet), so the probability that the cherry will be sweet is . CardsA standard deck of 52 playing cards consists of four suits (hearts, spades, diamonds and clubs). Spades and clubs are black while hearts and diamonds are red. Each suit contains 13 cards, each of a different rank: an Ace (which in many games functions as both a low card and a high card), cards numbered 2 through 10, a Jack, a Queen and a King.Certain and Impossible eventsAn impossible event has a probability of 0.A certain event has a probability of 1.The probability of any event must be Complementary EventsConsider the chance of an event not happening. Example (Complementary Events and Dice)What is the probability of not rolling a six on a six-sided die.Solution:To not roll a 6 on a six-sided die one would need to roll a 1 through 5. So the probability of not rolling a 6 would be ?.Consider another approach to this problem:The probability of rolling a 6 is ?. P(six) =?. Then consider the probability of rolling anything. The probability of rolling any number 1 through 6 would be 6/6 = 1. So the probability of rolling something not a 6 would be the probability of rolling anything minus (removing) the probability of rolling a 6. 1 - ? = ?. ?The probability of not rolling a 6 would be ?.U.S. Conversions:Example: ?Convert yards to feet.3 feet = 1 yard. ?Since we want to eliminate yards, we’ll put that in the denominator: = 13 feetMetric Conversions:Converting units in metric has the advantage that everything is multiplying or dividing by powers of 10, we can just move the decimal place.Example: ?Convert 24 centimeters to meters= 0.24 metersMultiple Conversions:Example: ?Convert 30 miles per hour to feet per minute.Multiplying, notice all the units cancel except feet on the top, and minutes on the bottom:= 2640 feet per minuteTemperature Conversions:To convert a Fahrenheit measurement to a Celsius measurement, use this formula.To convert a Celsius measurement to a Fahrenheit measurement, use this formula.Perimeter and Area:Volume:Measures of Central Tendency:The mean (sometimes called average) of a set of values is Example: Marci’s exam scores for her last math class were:? 79, 86, 82, 93.? The mean of these values would be: (79 + 86 + 82 + 93) divided by 4: Example: On three trips to the store, Bill spent $120, $160, and $35.? The mean of these values would be It would be most correct for us to report that “The mean amount Bill spent was $105 per trip,” but it is not uncommon to see the more casual word “average” used in place of “mean”.With some types of data, like incomes or home values, a few very large values can make the mean compute to something much larger than is really "typical".? For this reason, another measure, called the median is used.?To find the median, begin by listing the data in order from smallest to largest.? If the number of data values is odd, then the median is the middle data value.? If the number of data values is even, there is no one middle value, so we find the mean of the two middle values.Example:? Find the median of these quiz scores: 5 10 9 8 6 4 8 2 5 8We start by listing the data in order: 2 4 5 5 6 8 8 8 9 10Since there are 10 data values, an even number, there is no one middle number, so we find the mean of the two middle numbers, 6 and 8: ?.? So the median quiz score was 8.ModeThe mode of a set of data is the value that appears the most often.? If not value appears more then once, there is no mode.? If more than one value occurs the most often, there can be more than one mode.? Because of this, mode is most useful when looking at a very large set of data. ................
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