Math help !!!!!!!!!!!!!!!?
1. An airline had 122, 138, 114, and 133 passengers on four flights from San Diego to San Jose during 1 day. What was the total number of passengers? 2. You are fencing a backyard that measures 20 yd by 15 yd. How much fencing should you buy? 3. List all the prime numbers between 45 and 80 4. Find the prime factorization of the number 20. 5. Find two factors of 35 with a difference of 2. 6. Choose the correct greatest common factor of 28, 42, and 7. A used-car dealer sold 13 of the 52 cars in stock. What fraction names the portion sold? What fraction names the portion not sold. (Reduce fractions.) Please explain how to get the answers, Thank you
Mathematics - 7 Answers
Random Answers, Critics, Comments, Opinions :
1 :
1. Just add up all the numbers. 507 passengers. 2. A rectangle with long side of 20yd and a short side of 15yd. You need two lengths of each side = 40 + 30 = 70yd. 3. Look at the numbers and first of all cross off the even ones. You just have to check if they are divisible by any primes that are less than the square root of the number that you are checking. Since the largest number is 85, you just have to check 2, 3, 5 and 7. That leaves the following as primes ( they don't have 2, 3, 5 or 7 (or anything else) as factors): 47 53 59 61 67 71 73 79 83 4. You can really do this by inspection. Normally you divide by the lowest prime factor that fits (such as 2 or 3) and repeat until you have a prime. With 20, that's 2 x 2 x 5. 5. Well the two obvious factors of 35 are 5 and 7 (5x7=35) and they have a difference of 2. So - solved. 6. The greatest common factor of 28 and 42. Just list the factors and pick the greatest common one. 28: 2, 4, 7, 14 42: 2, 3, 6, 7, 14, 21 It looks like you had one more number that was missing from your question. Just list the factors for that and you can easily see the greatest common factor. The greatest common factor is 14. 7. 13 / 52 = 1 / 4 (divide top and bottom by 13) The portion not sold = 1 - 1/4 = 3/4
2 :
2. the perimeter is the lenght of all the sides added together. 20 + 20 + 15 + 15 = answer 5. 7 and 5
3 :
1. Just add them all up = 507 2. Perimeter of a rectangle is 2 * length + 2 * width=2*20+2*15=70 3. A prime number is a number that has exactly 2 factors, 1 and itself. Therefore, any even number greater than 2 is not a prime. So, consider only odd numbers greater than 45 and less than 80. You only have to check for divisibility for 3, 5 and 7 because they are the only prime numbers greater than 2 and less than or equal to 8.94427 (square root of 80). 49 is divisible by 7, 51 divisible by 3, 55 divisible by 5, 57 is divisible by 3, 63 is divisible by 3, 65 is divisible by 5, 69 is divisible by 3, 75 is divisible by 5, 77 is divisible by 7. That leaves 47, 53, 59, 61, 67, 71, 73, 79 4. 20 is even so divide by 2 to get 10. Even again, divide by 2 to get 5. 5 is a prime number so 2*2*5 5. 5 and 7 6. and? I see only 2 numbers. Prime factorization of 28 is 2*2*7 and the prime factorization of 42 is 2*3*7. The common prime factors are 2 and 7. 2*7=14 7. 13/52. Divide top and bottom by 13 (gcf) to get 1/4. The unsold cars are (52-13)/52 = 39/52. Divide top and bottom by 13 (gcf) to get 3/4.
4 :
1. to get the total number of passengers, add up those on each flight. 122 + 138 + 114 + 133 = 507 2. draw a picture of the backyard. (it is a rectangle). label the short sides 15 and the long sides 20. now add up the lengths of fence you need (15 + 20 + 15 + 20) = 70 3. prime numbers have no other factors except 1. So the even numbers are no good, nor are multiples of 3, 5, or 7. Taking these out leave 47, 53, 59, 61, 67, 71, 73, 79. Since the next prime after 7 is 11 and 80 is less than 11*11, these are all prime. 4. 20 = 4 * 5 - 2*2*5. 2 and 5 are prime, so we are done. 5. 35 = 1 * 35 = 5 * 7. 7 - 5 = 2. 6. gcd(28, 42, 7) is the largest number that divides all three without remainder. since 7 is prime, the only candidates are 1 and 7. 7 divides 28 and 42 evenly and it certainly divides 7 evenly, so it is the answer. {gcd = greatest common divisor, the same thing as greatest common factor) 7. 13/52 to simplify, divide numerator and denominator by 13 to get 1/4.
5 :
1.) ADD ; 122+138+114+133=507 passengers 2) 20x2+15x2=70 yrds, buy the cheapest/yard 3) 47,51,53,57,59,61,67,71,73,79 4) 2,4,5,10 5)7 and 5 ; 7-5=2 6) 7 7) 13/52= 0.25 x 100% = 25% 39/52=0.75 x 100% = 75% whew, hope it helps
6 :
2. you are finding the perimeter of the rectangle so you add up all the sides of the rectangle 2(20 yd) + 2(15 yd)= 70 yd. 3. a prime number is a number whose factors are only itself and one, meaning it has no other factors. some prime numbers between 45 and 80 include: 47, 59, 61... 4. break the 20 into two factors (10 x 2). 2 is a prime number so you continue by factoring the 10 (5 x 2). since 5 is also a prime number the answer is: 2 x 2 x 5. when writing the answer, you should always put the smallest number first. 5. 7 and 5. because 7 x5= 35 and 7-5= 2 7. fraction of portion sold= the # sold/ the total= 13/52= 1/4 portion not sold= the # not sold/ total= (52-13)/52= 39/52= 3/4 [you can also think about this as 1-(1/4) because the portion not sold is just the rest of the cars left, 100%- 25%=75%)
7 :
1. 122+138+144+133= 507 passengers in one day. 2. P= 2L + 2W P= 2(20) + 2(15) P= 40 + 30 P= 70 yds. 3. 47, 53, 59, 61, 67, 71, 73, 79 in this case, look up all multiples of 6 between 45 and 80 then subtract or add 1 to each no., but be careful. some are still composite with this (49, 55, 65,77) 4. 2x2x5 5. 1,5,7,35, so 7 and 5 6. 28= 2x2x7 42= 2x3x7 remove the 2 from 28 and the 3 from 42 then you get 2x7 or 14! 7. 25% and 75%
