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All Textbook Solutions for Mathematical Excursions (MindTap Course List)
37ES38ES39ES40ESUse the sieve of Eratosthenes procedure to find all prime numbers from 2 to 200. Hint: Because 20014.1, you need to continue the sieve procedure up to k=13. Note: You do not need to consider k=14 because 14 is not a prime number.42ES43ES44ESTwin Primes Find a pair of twin primes between 300 and 400. See Exercise 43.46ESGoldbach's Conjecture In 1742, Christian Goldbach conjectured that every even number greater than 2 can be written as the sum of two prime numbers. Many mathematicians have tried to prove or disprove this conjecture without succeeding. Show that Goldbach's conjecture is true for each of the following even numbers. 24 50 86 144 210 26448ES49ES50ES51ES52ES53ES54ES55ES56ES57ES58ES59ES60ES61ES62ES63ES64ES65ES66ES67ES68ES69ES70ES71ES72ESNumber of Divisors of a Composite Number The following method can be used to determine the number of divisors of a composite number. First find the prime factorization (in exponential form) of the composite number. Add 1 to each exponent in the prime factorization and then compute the product of these exponents. This product is equal to the number of divisors of the composite number. To illustrate that this procedure yields the correct result, consider the composite number 12, which has the six divisors 1, 2, 3, 4, 6, and 12. The prime factorization of 12 is 2231. Adding 1 to each of the exponents produces the numbers 3 and 2. The product of 3 and 2 is 6, which agrees with the result obtained by listing all of the divisors. Determine the number of divisors of each composite number. 36074ES75ES76ES77ES78ES79ES1EE2EE3EE4EEUse deductive reasoning to prove that every prime number is deficient.6EE1ESDetermine whether each number is perfect, deficient, or abundant. 32Determine whether each number is perfect, deficient, or abundant. 914ES5ESDetermine whether each number is perfect, deficient, or abundant. 144Determine whether each number is perfect, deficient, or abundant. 2048ES9ES10ES11ES12ES13ES14ESDetermine whether each number is perfect, deficient, or abundant. 26016ES17ES18ES19ES20ESIn 1876, Édouard Lucas proved, without the aid of a computer, that 21271 is a Mersenne prime.Use Euclid's procedure to write the perfect number associated with this prime.22ES23ES24ES25ES26ES27ES28ES29ES30ES31ES32ES33ES34ES35ESAmicable Numbers The Greeks considered the pair of numbers 220 and 284 to be amicable or friendly numbers because the sum of the proper divisors of one of the numbers is the other number. The sum of the proper factors of 220 is 1+2+4+5+10+11+20+22+44+55+110=284 The sum of the proper factors of 284 is 1+2+4+71+142=220 Determine whether 60 and 84 are amicable numbers. 1184 and 1210 are amicable numbers.37ES38ES39ES40ESFermat Numbers Numbers of the form 22n+1, where n is a whole number, are called Fermat numbers. Fermat believed that all Fermat numbers were prime. Prove that Fermat was wrong.42ESWeird Numbers Any number that is an abundant number but not a semiperfect number (see Exercise 42) is called a weird number. Find the only weird number less than 100. Hint: The abundant numbers less than 100 are 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, and 96.44ES1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13REWrite each Hindu-Arabic numeral in expanded form. 456,32715RE16RE17RE18REWrite each Babylonian numeral as a Hindu-Arabic numeral.20RE21RE22RE23RE24RE25RE26RE27RE28REWrite each Hindu-Arabic numeral as Mayan numeral. 52230RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88REWrite 3124 using Egyptian hieroglyphics.2TWrite the Roman numeral MCDXLVII as a Hindu-Arabic numeral.4TWrite 67,485 in expanded form.6TWrite the Babylonian numeral as a Hindu-Arabic numeral.Write 9675 as a Babylonian numeral.Write the Mayan numeral as a Hindu-Arabic numeral.Write 502 as a Mayan numeral.Convert 3542six to base ten.Convert 2148 to a. base eight and b. base twelve.13T14T15T16T17T18T19TDetermine whether 1001 is a prime number or a composite number.Use divisibility tests to determine whether 1,7327,285,147 is divisible by a. 2 b. 3, or c. 5.Use divisibility test to determine whether 19,531,333,276 is divisible by a. 4 b. 6 or c. 11.23T24T25TDraw the yin-and-yang symbol shown at the right. Hint: This symbol consists of multiple circles, each with its center on a vertical line.2EE3EEDraw the heart-shaped figure shown at the right. Here is a suggestion on how to begin. First, use the construction shown at the far right to draw a right triangle. Then bisect the angle and draw some circles.1ES2ESConvert between the two measurements. 5yd = in.4ES5ES6ESConvert between the two measurements. 712 lb = oz8ES9ES10ES11ES12ES13ES14ES15ES16ES17ES18ES19ES20ES21ES22ES23ES24ES25ES26ESSolve. Round to the nearest hundredth if necessary. Express 30 mi/h in kilometers per hour.Solve. Round to the nearest hundredth if necessary. Seedless watermelon costs $0.59/lb. Find the cost per kilogram.29ESSolve. Round to the nearest hundredth if necessary. Find the weight, in pounds, of an 86-kilogram person.Solve. Round to the nearest hundredth if necessary. Find the width, in inches, of 35-mm film.32ES33ESSolve. Round to the nearest hundredth if necessary. A 2.5-kg bag of grass seed costs $10.99. Find the cost per pound.35ES36ES37ESAs our scientific and technical knowledge has increased, so has our need for ever-smaller and ever-larger units of measure. The prefixes used to denote some of these units of measure are listed in the table below. These new units of measure are quickly working their way into our everyday lives. For example, it is quite easy to purchase a 1-terabyte hard drive. One terabyte (TB) is equal to 1012 bytes. As another example, many computers can do multiple operations in 1 nanosecond (ns). One nanosecond is equal to 109 s. Convert between the two units. 9.46 a = _____39ES40ES41ESA light year is approximately 6,000,000,000,000,000 mi. Describe a light year using Ym (yottameters).In the 1980s, it became possible to measure optical events in nanoseconds and picoseconds. Express 1 Ps as a decimal.44ES1EEPrepare a circle graph for the data provided in each exercise. A survey of children between 10 and 14 years old was conducted to determine the average amount of tune they spent consuming media each day. The results are shown in the table below.1ESState the number of degrees in a full circle, a straight angle, and a right angle.3ES4ES5ES6ES7ES8ES9ES10ESGiven AB = 12 cm, CD = 9 cm, and AD = 35 cm, find the length of BC.12ES13ES14ESGiven in mLOM=53 and in mLON=139, find the measure of MON.Given in mMON=38 and mLON=85, find the measure of LOM.17ES18ESGiven that LON is a right angle, find the measure of x.Given that LON is a right angle, find the measure of x.21ES22ES23ES24ES25ES26ES27ES28ES29ES30ES31ES32ES33ES34ESGiven that l1l2, find the measures of angles a and b.36ESGiven that l1l2, find the measures of angles a and b.Given that l1l2, find the measures of angles a and b.Given that l1l2, find x.40ES41ES42ESGiven that ma=95 and mb=70, find the measures of angles x and y.Given that in ma=35 and mb=55, find the measures of angles x and y.