# prime

1,414 results, page 12

### math

There are 24 students in Mr.Hills class. The number of boys and number of girls are both prime numbers. There are 2 more boys then girls. How many boys and how many girls are in each class?

### math

List all possible rational zeros of... h(x)= 2x to the (4th power) - 5x (to the third power) + 3x (to the 2nd power) + 4x - 6 Use the Rational Roots Theorem. Any root of the form p/q with p and q relatively prime must be such that p divides 6 and q divides 2. You then find the...

### Environmental Science

India’s prime minister puts you in charge of that nation’s population policy. India has a population growth rate of 1.6% per year, a TFR of 2.7, a 49% rate of contraceptive use, and a population that is 71% rural. What policy steps would you recommend, and why? What do ...

### math

Megan factored the expression (-12x^2+52x-35) as (-2x+5)(6x-7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x-7) he got (-12x^2+44x-35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and ...

### math

Megan factored the expression (-12x^2+52x-35) as (-2x+5)(6x-7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x-7) he got (-12x^2+44x-35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and ...

### algebra

Megan factored the expression (-12x^2+52x-35) as (-2x+5)(6x-7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x-7) he got (-12x^2+44x-35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and ...

### algebra

Megan factored the expression (-12x^2+52x-35) as (-2x+5)(6x-7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x-7) he got (-12x^2+44x-35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and ...

### algebra

Megan factored the expression (-12x^2+52x-35) as (-2x+5)(6x-7) but when Jacob applied FOIL principle and multiplied out (2x+5)(6x-7) he got (-12x^2+44x-35),thus megan's solution does not appear to check please help megan to understand better.Explain your reasoning and ...

### Math

5.Mrs.Sandoval has 60 folders, 45 scissors, and 30 rulers. What is the largest number of equally divided school supply groups Mrs.Sandoval can create without any remaining supplies? A.5 B.10 C.3 D.15 D 6.What is the prime factorization of 550? A.2x5^2x11 7.What is the value of...

### probability

two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the following events. A:the sum ...

### Math

I don't have any specific problems I need help with, but I'm a bit confused about two things: 1) Where 2^x - 1 = y, is x or y the Mersenne prime? 2) I have noticed that in some cases, such as 27 * 3, I can break the problem up and arrive at the correct result: 27 * 3 = 81 (20...

### Arithmetic

Hi, i'm preparing for Olevels and i have some maths questions that i'm not sure how to do, i'd appreciate it if you could help. 1. The numbers 60 and 126, written as products of their prime factors: 60=2^2x3x5 126=2x3^2x7 a)Find the largest integer which is a factor of both 60...

### math

21.a. which of these number is a multiple of 10? A 35 B 40 C 45 D 101 b. how can you fine the answer for part a just by looking? 22.a. A dime is what fraction of a dollar? b. A dime is what percent of a dollar? 23. washington school cost about \$12,350,000 to build. use words ...

### math

A student claims that every prime greater than 3 is a term in the arithmetic sequence whose nth term is 6n + 1 or in the arithmetic sequence whose nth term is 6n - 1. Is this true? if so, why?

### prealgebra

One letter is randomly selected from the word PRIME and one letter is randomly selected from the word MATH. What is the probability that both letters selected are vowels?

### Macdonald

I don't understand this He was the dominant creative mind which produced the BRITISH NORTH AMERICA ACT and the union of provinces which became Canada. As the first prime minister of Canada, he oversaw the expansion of the Dominion from sea to sea. His government dominated ...

### Intermidia Algebra

Andrew factored the expression -12x^3-28x^2-3x as -4x (3x^2-7x+9). But when Melissa applied the distributive law and multiplied out -4x (3x^2-7x+9), she got -12x^3+28x^2-36x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this...

### Math

4 students each wrote 2 number patterns Shandi 3,6,9,12... 5,15,20,25 Latrell 1,3,5,7...3,5,7,9 Hong-Li 0,1,3,6...1,2,4,7 Adriano 2,3,5,7...11,13,17,19 Which student's number patterns used only prime numbers? A.Shandi B.Latrell C.Hong-Li D.Adriano D?

### English

Here are the last paragraphs on history Thank you very much for helping me!! 1) The first political parties were the Whigs and the Tories. The Whigs descended from the Parliamentarians. 2) They were in power continuously from 1714 to 1760 and pressed for industrial and ...

### Math

Freddy and his friends write their names in code. Each friend's name is represented by a number. To identify the friend in a message, you must find the prime factorization of the number. Freddy gets a message from 45. Who is the message from. Secret Code: Freddy= 2x3x5 Judy= ...

### math

The LCM of two numbers is 51. Both numbers are greater than 1 and both numbers are prime. What are the two numbers?

### FINANCE

Carborundum Metals issues commercial paper with a face value of \$1,000,000 and a maturity of three months. Carborundum receives net proceeds of \$992,000 when it sells the paper. If the prime rate is 8% APR compounded quarterly, how much savings in interest did Carborundum ...

### Finance

Carborundum Metals issues commercial paper with a face value of \$1,000,000 and a maturity of three months. Carborundum receives net proceeds of \$992,000 when it sells the paper. If the prime rate is 8% APR compounded quarterly, how much savings in interest did Carborundum ...

### math

in a game you draw a card with three consecutive numbers on it. You can choose one of the numbers and find the sum of its prime factors. then you can move that many spaces. You draw a card with numbers 25, 26, 27. Which number should you choose if you want to move as many ...

### calculus

The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have no clue how to solve this I know the ...

### calc

The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have no clue how to solve this I know the ...

### math

For every prime p consider all polynomials f(x) with integer coefficients from 1 to p and degree at most p−1, such that for all integers x the number f(2x)−f(x) is divisible by p. Find the sum of all primes p<1000 such that the number of such polynomials is ...

### math

For every prime p consider all polynomials f(x) with integer coefficients from 1 to p and degree at most p−1, such that for all integers x the number f(2x)−f(x) is divisible by p. Find the sum of all primes p<1000 such that the number of such polynomials is ...

### Algebra

Andrew factored the expression 20x^3-12x^2+8x as 4x (5x^2-12x^2+8x). But when Melissa applied the distributive law and multiplied out 4x (5x^2-12x^2+8x), she got 20x^3-48x^3+32x^2; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to ...

### algebra

Andrew factored the expression 20x^3-12x^2+8x as 4x(5x^2-12x^2+8x). But when Melissa applied the distributive law and multiplied out 4x(5x^2-12x^2+8x),she got 20x^3-48x^3+32x^2; thus, Andrew's solution does not appear to check. Why is that? Please help Andrew to understand ...

### Computer Science

public class PrimeNumbers { public static void main(String[] args) { int x = 100; for(int i=2; i <= x; i++) { if(i%2==0) System.out.println("notprime"); System.out.println(i) ; if(i%1==1) System.out.println("prime"); } }

### math

three of these puzzles have more than one answer. try to find all the possible answers for each puzzle one of these puzzle is impossible. 1.my number is a factor of 20. it's also a factor of 30. 2. my number is a multiple of 10. it's a factor of 45. 3. my number is between 40 ...

### math

The sum of my ones and tens digit is 10. My tens digit is greater than my ones digit. I am a prime number. What number am I?

The sum of my ones digit and tens digit is 10. My tens is greater than my ones digit. I am a prime number. What number am I?

### MATH HELP

Zoro Manufacturing Company manufacturers wooden picture frames. Each piece of wood yields 15 frames. Each piece of wood costs \$18.75. The direct labor charge is \$13.50 per hour. Sixty-five frames can be produced each hour. To the nearest tenth of a cent, what is the prime cost...

### math

answer these or you don't have to just need some help? 13. Which set of numbers has 270 as its least common multiple? A.30, 90, 390 B.18, 30, 54 C.25, 125, 120 D.2, 9, 15 14. Which list shows the numbers in order from greatest to least? A.16, 8, 4, –12, –15 B.–12, –15...

### Calc- Derivatives

So, I have a bunch of derivative problems for homework and the only resource I have is the textbook, since we don't have notes. I have just started and want to make sure I'm doing them correctly. Our teacher said we do not have to simplify them either, so I'm also confused if ...

### geography

Thank You and I did some more questions. Can you check them? 1. Is the Antarctic Circle north or south of the equator? South of the equator 2. All lines of longitude are measured east and west of what imaginary line? The Prime Meridian. Ms. Sue the 9th grade Algebra question I...

### Algebra

Directions: Find the prime factors of the polynomials 1. a. 2a2 - 2b2 b. 6x2 - 6y2 c. 4x2 - 4 d. ax2 - ay2 e. cm2 - cn2 2. f. st2 - s g. 2x2 - 18 h. 2x2 - 32 i. 3x2 - 27y2 j. 18m2 - 8 3. k. 12a2 - 27b2 l. 63c2 - 7 m. x3 - 4x n. y3 - 25y o. z3 - z 4. p. 4c3 - 49c q. 9db2 - d r...

### math

A red die and a green die have been rolled. (6 sided) What is the probability of the event? 1.The number on the red die is greater than the number on the green die (Answer is 5/12 but how?) 2. The sum is less than 10. 3. The sum is even. 4. The sum is prime. 5. The sum is 7 or...

### Algebra

I need help trying to put the correct vocabulary words when solving this problem such as grouping, factor, prime factor, GCF, and perfect square, and please check and see if I am doing this correctly. 15x^2+31x+2 In my last problem I will be using the “ac method” A*C = 15*...

### Geometry

I need help with counterexamples and all the questions are false. 1.If an angle measures 34 degrees ,then the angle is acute. 2.If the length of twwo segments are each 17 feet,then the segments are congruent. 3.If two angles 32 and 148 degrees ,then are supplementary. 4.If you...

Check my answer and if it is not right, what is it?: How did China become a communist nation? The communists were elected. The communists gained control after a long civil war. The communists gained control in a swift coup d’état. The emperor appointed a communist prime ...

### Algebra 2 ..

Please explain on how to do each of these! *Let (x) be defined for all positive integer values of xas the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT GET HOW THEY ARRIVED THAT...

### Computer Science

I need some help about Turing Machines, and prove by reductions. Here are the 2 questions: 1. Sketch the construction of a Turing Machine that decides the language L = a^i where i is not prime. 2. Show that the language 2Strings is not recursive by reducing any one of the two ...

### statistics

A card is to be chosen at random from a shuffled deck. Find the probability that the card drawn is a)the queen of clubs, given that it is an honor card. (I think it is a typo) b) a red four, given that the face number is even. c) a seven, given that the face number is prime. ...

### bio stats

n a Star Trek episode, a population of tribbles (average weight of 56 grams) invade a Klingon starship. The Klingons enjoy eating the tribbles they can find. A Romulan spy smuggles the remaining tribbles (average weight of 21 grams) to Romulus prime. The offspring of the ...

### algebra 2

What is the 20th term of the sequence that begins -3,6,-12,24? A. 524,288 B 524,288 C. 1,572,864 d. 3,145,728 The term in a geometric sequence is 160. the 7th term is 40. What are the possible values of the 6th term of the sequence? You roll a standard, six sided number cube. ...

### factorization

In a game, you draw a card with three consecutive numbers on it. You can choose one of the numbers and find the sum of its prime factors. Then you can move that many spaces on a game board. You draw a card with the numbers 25, 26, 27. Which number should you choose if you want...

### math

how to use hundreds chart to answer this;(1)what % of the numbers are multiples of 3 (2)what % of the numbers are multiples of both 2 and 3 (3) what% of the numbers are factors of 100 (4)what % of the numbers are prime numbers? i really have no idea how to use hundreds chart ...

### math

In a game, you draw a card with three consecutive numbers on it. You can choose one of the numbers and find the sum of its prime factors. Then you can move that many spaces on a game board. You draw a card with the numbers 25, 26, 27. Which number should you choose if you want...

### Maths!

There has just been a planetary alignment of five planets in the system Blogg, all the astrologers have gone loopy, and they want to know when the next occurance of these five planets will happen again. Krypton the nearest planet to the sun takes 6 days to orbit the sun. Zenon...

### math

Find the mystery number im a number between 300 and 400 im divisible by 3 and 4 . but not 9 my tens digit is a square number the sum of the hundreds digit and the tens digit is a prime number. find the mystery number

### Math

A six sided die is tossed. What is the probability that it shows a prime number if you know the following? a. It shows an even number. b. It shows a number less than 5. c. It does not show a 6. d. It shows 1 or 2/ e. It shows an even number less than 4. f. It shows a number ...

### Algebra

Can someone help me with this please. Andrew factored the expression 20x^3-12x^2+8x as 4x(5x^2-12x^2+8x) but when melissa applied the distributive law and multiplied out 4x(5x^2-12x^2+8x)she got 20x^3-48x^3+32x thus Andrews solution does not appear to check. Why is that? ...

### math

the spinner shown to the right has 8 equal sized sections labeled 1 through 8 place the probability of each outcome described below on the number line identify each outcome as likely unlikely or neither likely nor unlikely 1. arrow lands on 8 2. arrow lands on number greater ...

### math

Three of these puzzles have more than one answer. Try to find all the possible answers for each puzzle. One of these puzzles is impossible. 1.My number is a factor of 20.It's also a factor of 30. 2.My number is a multiple of 10.It's also a factor 45. 3.My number is between 40 ...

### geography

Does the prime Meridian pass through the North or South Pole? I put it does not pass through either the North or South Pole. My teacher marked it wrong and said it passes through both. Can you please let me know if I am right and give me a web sight I can go to so I will have ...

### 5th Grade Math - Urgent Part II

Sorry my question got cut off. 2 to the 6th power times 5 to the 6th power equals 1,000,000. Is there another number that has the prime factorization 2 to the 6th power times 5 to the 6th power? Are you saying the other number that has the same factorization is 64?

### Algebra

I need help trying to put the correct vocabulary words when solving this problem such as grouping, factor, prime factor, GCF, and perfect square, and please check and see if I am doing this correctly. 15x^2+31x+2 In my last problem I will be using the “ac method” A*C = 15*...

### A proof question

Suppose 32 = alpha*beta for alpha, beta reatively prime quadratic integers in Q[i] . Show that alpha = epsilon*gamma^2 for some unit epsilon and some quadratic integers gamma in Q[i]. If you know how , please do teach me . Thank you .

### geography

Can you check my answers? 1. Locate the Gulf of Aden off the eastern coast of Africa. Now, write a definition of a gulf? A gulf is a part of an ocean or sea that extends into land. 2. What lines measure distances east and west of the Prime Meridian? Meridians or lines of ...

### math

the number of 5th grade students in a school is a prime number greater than 50.What is the least number of 5th grade students there could be in a school

### MATH

1. Evaluate. 54 divied (42 + 2) 2. Evaluate 120 cal/g x 4 g. Be sure to use the proper units. A) 480 g B) 480 g/cal C) 480 cal D) 480 cal/g 3. Prime numbers that differ by 2 are called twin primes. Examples are 3 and 5, 5 and 7, and so on. Which pair of numbers are twin primes...

### Social Studies definition

Presidential- legislative: An elected president leads the government, sharing power with a legislature and with the courts. ( the US is an example of a presidential-legislatie democracy) Question: Which best describes presidential-legislative? a. courts have little power b. ...

### Health of young children

A teacher is in a prime position to observe children because A.the teacher sees children in relation to other children of the same age. B. the teacher sees each child for fewer hours than the parent and can, therefore be objective. C.he or she is often involved in children's ...

### math

determine the next three numbers in this pattern: 2,3,5,7,11,13,17,19,23,___,___,___ Aren't these all prime numbers? Find the next three numbers in the pattern. 5,2,-1,-4 3,2,0,-3,-7 -8,-6,-2,4,12 -5,-7,-8,-10,-11

### Algebra

what is the value of (n) ? (n+3)! = 5040 the prime factorization of 5040 = 2x2x2x2x3x3x5x7 since the ! function involves the multiplication of consecutive integers, it makes sense to arrange these factors so they form consecutive numbers. I got 2,3,4,5,6, and 7 and sure enough...

### math

Get the number right. *None of the digits repeat. *It is between 20,000 and 77,777 *The digit in the thousands place is 3 times the digit in the ten thousands place *The ones digit is a prime number *The hundred digit is half the sum of the ones, thousands, and tan thousands ...

### math

List the ages of two people in your life, one older than you and one younger than you. It would be best if the younger person was 15 years of age or younger. Find the prime factorizations of your age and the other two persons’ ages. Show your work listed by name and age. ...

### Calculus

A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your answer I think you have to find the prime ...

### Calculus

A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your answer I think you have to find the prime ...

### Calculus!!!!

A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your answer I think you have to find the prime ...

### SS HELP PLZ

1)Which of the following does NOT concern dividing up the earth into smaller sections? A. Parallels B. Meridian C. Cardinal Directions**** D. Hemispheres 2)Which of the five themes includes human and physical features at a specific location? A. Locations B. Place**** C. ...

### Math.

#1) Consider the experiment of rolling a single die. Find the probability of the event described. What is P(odd and prime)? A) 1/6 B) 1/2 C) 1/3 D) 2/3 #2) Consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of ...

### Geo

How does latitude and Longitude affect the climate in St.Jonh. I don't get it??? St.John New Brunswick I mean. The longitude doesn't affect St. John's climate since it measures distance from east and west from the Prime Meridian. However, its latitude, about 45 degrees N, ...

### Calculus - Still Need Help! Anyone!

A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi. a) Find the time t at which the particle is farthest to the left. Justify your answer I think you have to find the prime ...

### HISTORY

By the end of the 1800's jobs employed ____________ between the ages of 10 and 16? Who owned much of the Western land near prime transportation routes? What fraction of the soldier's out West deserted? Child Labor was the scourge and economic engine of the time. I guess: the ...

### math

im having trouble with radicals, we learned them today but our teacher dint go over what to do with fractions, could u tell me what to do in the square root of 5/36? thx again sqrt (5/36) = (sqrt 5)/sqrt36 = 1/6 * sqrt5 The square root radical applies to both the numerator and...

### Math

Hi. I found this question on a Math Counts practice test and it seriously confused me. I've never learned about this, and it would help if someone helped me. Thanks in advance. How many elements are in the intersection of the set of all the prime numbers less than 30 and the ...

### S.S

1. Which resource makes up a quarter of Chile's exports? (1 point)fruit fish copper silver 2. Chilean produce is free of many common plant pests because most farming regions are protected by the (1 point)Atacama Desert. Andes Mountains. Amazon River. Strait of Magellan. 3. ...

### math

Tony and Tom are brothers.This year both of their ages are prime numbers. Last year both of their ages were composite numbers. Both of their ages will be composite numbers again over the next three years. If Tony and Tom are both teenagers, how old are they now?

### math

Joel and jacob are brothers. This year both of their ages are prime numbers. Last year both of their ages were composite numbers.Both of their ages will be composite numbers again over the next three years. If joel and jacob are both teenagers, how old are they now?

### Math 1350

Mrs. Jones has a prime number of children in her class. When she divides the children into teams of 7, one team has 6. When she divides the children into teams of 6, one team has 5. How many children are in the class?

### math

the number has 7 digits it is evenly divided by 00 the value of one of the digits is 60,000 the digit in the hundredth place is both even and prime the digit is the thousands place is 1/2 the value of the digit in the ten thousand place the digit in the hundred thousands place...

### geography

I just wanted to make sure my answers are correct, Can you check it please? Find an example of an area of land that is smaller than a continent and is completely surrounded by water. What term is used to describe this type of land? An example is Jamaica. The term that is used ...

The number has 7 digits It is evenly divisible by 100 The value of one of the digits is 60,000 The digit in the hundreds place is both even and prime The digit in the thousandr place is half the value of the digit in the ten thousands place The digit in the hundred thousands ...

### AP Biology

In 1918 a particularly virulent strain of influenza (an RNA virus) wiped out millions of health humans in the prime of their lives. Epidemiologists fear that such a super bug could revisit us in the future. And thus there was quest to find samples of the virus, and make a ...

### Math

I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k ≠ 1 so log2√36...

### Math

I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k ≠ 1 so log2√36...

### Math

I don't understand how log2 √(1/2) turned into log2 2^(-1/2). Quote: You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k ≠ 1 so log2√36...

### RELIGION

One might do good amal deeds in the intention of getting the reward of Jannah. However, some ulama prefer a person to do for the love and gratitude towards Allah rather than seeking Jannah. So,perhaps the best thing to do is to focus primarily on doing good amal for the love ...

### islam

One might do good amal deeds in the intention of getting the reward of Jannah. However, some ulama prefer a person to do for the love and gratitude towards Allah rather than seeking Jannah. So,perhaps the best thing to do is to focus primarily on doing good amal for the love ...

### math

There are 3 red balls and 7 blue balls in Bowl A, and 8 red balls and 2 blue balls in Bowl B. Mandy rolls a die and if a prime number is up, Bowl A is selected; otherwise Bowl B is selected. Then Katie draws a ball randomly from the selected bowl. Find the probability of Bowl ...

### ALGEBRA 2...

*Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT GET HOW THEY ARRIVED ...

### Algebra 2.....

*Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT GET HOW THEY ARRIVED ...

### Fin

Midland Chemical Co is negotiating a loan from Manhattan Bank and Trust. The small chemical company needs to borrow \$500,000. The bank offers a rate of 8¼ percent with a 20 percent compensating balance requirement, or as an alternative, 9¾ percent with additional fees of \$5,...

### math

Something times something equals 97 Are you supposed to factor 97 as the product of integers? We need a little more info to help you. If you are expecting integer results, wait no more as 97 is a prime number. Therefore, no two integers have a product of 97. If you are not ...

### Big Data

Suppose our input data to a map-reduce operation consists of integer values (the keys are not important). The map function takes an integer i and produces the list of pairs (p,i) such that p is a prime divisor of i. For example, map(12) = [(2,12), (3,12)]. The reduce function ...