MATH 1030Review for Exam #1 Solutions1. Betty looks through her stack of scratch paper and records the following information regardingthe scratch paper.- 214 sheets of paper.- 130 of them are lined- 140 of them are white- 50 of them have some writing on them- 110 of the lined paper are white- 12 of the lined white paper have writing on them- 25 of the white paper have writing on them- 20 of the lined paper have writing on themDraw a Venn diagram to describe this information and use it to determine how many sheets ofpaper Betty has that are either white or lined (this includes those that are both).1217 138 98linedwhitew/ writing171237So there are 214 − 37 − 17 = 160 sheets of paper that are white or lined.12. Steve Keyboard works in an office building. He finds out the following information regardingthe 68 people on his floor.- 25 can type over 75 words per minute- 24 have a college degree- 32 bring sack lunches- 13 of the college graduates bring sack lunches- 13 of the college graduates can type over 75 words per minute- 13 of those that type over 75 words per minute bring sack lunches- 5 of the college graduates that bring sack lunches can type over 75 words per minuteDraw a Venn diagram to describe this information and use it to determine how many peoplethere are in the office who do not bring sack lunches, do not type over 75 words per minute, butdo have a college degree.8458811 32175 wpmcollege degreesack lunchSo there are 3 college graduates who do not bring sack lunches and do not type 75 wpm.23. Determine whether the following deductive argument is valid or invalid. If it is valid, determinewhether or not the argument is sound.Premise #1: All dwarf planets have mass less than one hundredth times the mass of the earthPremise #2: The mass of Ceres is less than one hundredth times the mass of the earthConclusion: Ceres is a dwarf planetLet A be the set of all dwarf planets and let B be the set of all objects whose mass is less than1/100th times the mass of the Earth. Then A is a subset of B by the first premise and thediagram for the argument is:ABxSo the argument is invalid because it cannot be determined whether Ceres is in A or not.4. Determine whether the following deductive argument is valid or invalid. If it is valid, determinewhether or not the argument is sound.Premise #1: Every region with pyramid structures was home to an ancient civilizationPremise #2: Cydonia is a region of Mars with pyramid structuresConclusion: Cydonia was home to an ancient civilizationLet A be the set of regions with pyramid structures and let B be the set of regions that werehome to an ancient civilization. Then A is a subset of B by the first premise and the diagramfor the argument is:ABxSo the argument is valid since Cydonia is necessarily in B. It is not sound, since the first premiseprobably is not true.5. Suppose Maxine’s car gets 35 miles per gallon. What is her fuel efficiency in feet per fluid ounce?( 128 fluid ounces = 1 gallon, 1 mile = 5280 feet )35migal1 gal128 oz5280 ft1 mi= 1, 443.75ftoz36. It is estimated that when the natural dam at Red Rock Pass broke, water from Lake Bonnevilleat a rate of 15,000,000 cubic feet per second. Compute the flow rate of the water in cubic milesper day.( 1 mile = 5280 feet, 1 hour = 3600 seconds, 1 day = 24 hours )15, 000, 000ft3sec1 mi5280 ft1 mi5280 ft1 mi5280 ft3600 sec1 hr24 hr1 day= 8.804mi3day7. Outer space sales tax just increased to 3.8%. If Petra’s astronaut ice cream cost $12.44 afterouter space tax, how much did her ice cream cost before tax?So 12.44 is 3.8% more than the price before tax. If x is the price before tax, then 12.44 is 103.8%of x; that is,12.44 = 1.038x12.441.038= x11.98 = xSo the price before tax was $11.98.8. Last year Jupiter Space Suits cost $1,485. This year Jupiter Space Suits cost $1,678. By whatpercent did the cost of Jupiter Space Suits increase from last year to this year?We want to know: 1,678 is what percent more than 1,485.1, 678 = x(1, 485)1.1299 = xSo 1,678 is 112.99% of 1,485, meaning that 1,678 is 12.99% more than 1,485; that is, the cost ofthe suits increased by 12.99%.9. The outer space economy is very unpredictable. Two years ago, outer space inflation caused thevalue of outer space currency to increase by 2.1%. Last year, the value of outer space currencyincreased by 6.3%. This year, the value of outer space currency decreased by 8.8% due to thebanking collapse. Find the total percentage increase or decrease over the last two years.A 2.1% increase corresponds to multiplying by 1.021. A 6.3% increase corresponds to multiplyingby 1.063. A 8.8% decrease corresponds to multiplying by .912. So the total change correspondsto multiplying by(1.021)(1.063)(.921) = .9898so the total change is a net decrease by 1.02%.410. Laura just sold a really fancy sweater she knitted out of vicu˜na wool she spun herself from herown vicu˜na farm in Peru. She made $3000. Now she wants to deposit it in a bank account.Chevy Chase Bank is offering 4.11% APR compounded monthly, and the Banco de Cr´edito delPeru is offering 4.1% APR, compounded continuously.(a) If she puts her money with Chevy Chase Bank, how much will she have in 10 years?A = 3, 0001 +.041112(12)(10)= 4, 521.80(b) If she puts her money with Banco de Cr´edito del Peru, how much will she have in 10 years?A = 3, 000e(.041)(10)= 4, 520.45(c) Calculate the APY for each account. Which is the better account?For the Chevy Chase Bank account,1001 +.04111212= 104.1883so the APY is 4.1883%.For the Banco de Cr´edito del Peru account,100e.041= 104.1852so the APY is 4.1852%.The Chevy Chase Bank account is better.(d) Suppose she puts her money in the better account. In 10 years, what percentage of herbalance will be from interest?In the better account, Laura ends up with $4,521.80. $3,000 of it was deposited, so $1,521.80came from interest. We want to know: 1,521.80 is what percent of 4,521.80.1521.80 = x(4521.80).3365 = xSo 1,521.80 is 33.65% of 4,521.80.11. Arjen wants to have $40,000 21 years from now. His savings account has an APR of 5.3%,compounded daily.(a) How much should he deposit now in order to reach his goal?40, 000 = P1 +.053365(365)(21)40, 000 = P (3.043229017)13, 143.93 = PSo Arjen needs to deposit $13,143.93 in the bank right now.5(b) By what percent did his deposit increase in the 21 years?He deposits $13,143.93 and ends up with $40,000. We want to know: 40,000 is what