Prove that for a,b,c belongs to natural numbers, if a+b+c is divisible by 30 so is a^5+b^5+c^5.
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Math
Determine whether the event is impossible, unlikely, as likely as not, likely, or certain. Then tell whether the probability is 0, close to 0, 1/2, close to 1 or 1. Picking a number that is divisible by 5 from a jar with papers labeled from 1 to 12. The

arithmetic
Prove that the product of three consecutive even numbers is divisible by 48

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List all the numbers from the given set that are, a.natural numbers b.whole numbers c.integers d.rational numbers, e.irrational numbers {9,4/5,0,0.25,ã3,9.2,ã100}

AiMS MATH
5 Is A Member Of Which Subset Of Real Numbers. a) natural numbers b) whole numbers c) intergers d) rational numbers e) irrational numbers

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Are the following true or false? 1. The difference of two natural numbers is always a natural number. 2. The sum of two natural numbers is always a natural number. 3. The quotient of two natural numbers is always a natural number. 4. The difference of two

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Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³  5(1) = 6, which is divisible by 6 Then I really

Algebra
Choose which group of sets the following number belongs to. Be sure to account for ALL sets. 2/5 A. Real numbers, rational numbers. B. Real numbers, irrational numbers. C. Rational numbers, natural numbers, integers. D. Irrational numbers, natural numbers.

math problem
My ID number is quite remarkable.Its a 9 digit number with the digits 19 appearing only once. The entire 9 digit nuymber is divisible by 9. If you remove the last digit, the remaining 8 digit number is divisible by 8. If you remove the last digit again,

9th grade
Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above my answer a)rational numbers

new math
Tell whether each number is divisible by 2, 3, 4, 5, 8, 9, or 10. Some numbers may be divisible by more than one number. 1.324 2.840 3.2,724 4.81,816 5.7,848

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Classify the square root of 17 by the subsets of the real numbers to which it belongs select all that apply. Whole rational real natural integer irrational

math
can somebody help me to check my answer Identify if the first number is divisible by the second number, and if so, the reason why. Is 216 divisible by 3? A. No B. Yes, because the sum of 2 + 1 + 6 = 9, which is divisible by 3. C. Yes, because the last

math
PLEASE HELP THIS IS DUE TODAY!!! Which number is divisible by 2, 9, and 10 A. 45 B. 60 C. 90 D. 150 Which of the following numbers is divisible by 2, 3, 5, 6, 9, and 10? A. 420 B. 540 C. 250 D. 510 45 is divisible by which of the following numbers? A. 1,

math
three digit numbers are to be formed from digits 0,1,2,3...9 if repetitionis allowed. (a) how many of such numbers can be formed? (b)how manyof the numbers in(a)are divisible by 3 and how many of 9? (c) find the sum of all the numbers divisible by 3 but

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Choose all the sets containing the number –1.576. natural numbers whole numbers integers rational numbers irrational numbers real numbers

Math help Ms. Sue please
1. Name the subset(s) of real numbers to which the number zero belongs. You can choose more than one answer. Irrational numbers Integers Whole numbers Natural numbers 2. Write an algebraic expression for the word phrase: the quotient of r and 12. r * 12 r

Math
prove that the difference of squares of any two odd numbers is divisible by 4. (first list at least 3 examples to support this statement.)

Mathematical Induction
Use mathematical induction to prove that the following is true. 8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers.

9th grade alebra
Name the set of numbers to which 10 belongs A whole numbers , integers , rational numbers B rational numbers C integers or rational D whole numbers , natural numbers , integers

math
List all the numbers given set that a natural numbers be whole numbers c integers d rational numbers e irrational numbers f real numbers

Math
Use mathematical induction to prove that 5^(n)  1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, 1 = 5 +4 This is a take home test so I don't want the answer because I want to know

maths
A positive integer n is such that numbers 2n+1 and 3n+1 are perfect squares. Prove that n is divisible by 8. thanks

math
Which statement about numbers is true? A: All integers are natural numbers. B: All rational numbers are integers. C: All natural numbers are whole numbers. D: All rational numbers are natural numbers.

Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1)  2^5(1) = 7, which is divisible by 7. For the inductive case, assume k ≥ 1, and the result is true

Math
Name the set(s) of numbers to which 10 belongs Whole numbers, integers, rational numbers ** Integers, rational numbers Whole numbers, natural numbers, integers Rational numbers

Math
If a natural number is divisible by 7, then it must also be divisible by 21.

math
Choose all true statements. All real numbers are rational numbers. Some rational numbers are natural numbers. No real numbers are irrational numbers. All whole numbers are integers. Some integers are natural numbers. No rational numbers are integers.

Algebra ASAP
so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers n. Let P(n) denote the

math
1.62 is divible by which of the following numbers? A.1,3,31,62 B.1,2,3,31 C.1,4,16,62 D.1,2,31,62 I PICKED D.  2.108 is divisible by which of the following sets of numbers? A.1,2,3,4,6,9,12,18,27,36,54,108 b.1,2,4,27,54,108

Math
How many threedigit counting numbers are exactly divisible by 6 but not also exactly divisible by 9?

Math
Which expression is equivalent to (2)(a+6)? 2a+6 2a+12*** 2a12 2a+12 To which subsets of real numbers does the number 22 belong? Choose all that apply. Whole numbers*** rational numbers integers*** irrational numbers "6 times the difference of b and

Math
1. Is 26 divisible by 2? A. No. B. Yes, because 2 + 6 = 8 and 8 is divisible by 2. C. Yes, because the last digit is 6, which is divisible by 2. 2. Is 216 divisible by 3? A. No. B. Yes, because the sum of 2 + 1 + 6 = 9, which is divisible by 3. C. Yes,

Math
Name ALL sets of numbers to which each number belongs Real, Rational, Irrational, Integer, Whole, Natural 5/6

Math
Given the digits 1,2,5,7,8,9,0 and if repetition are not allowed, answer each of the following: A) how many 3 digit numbers canbve formed that are divisible by 5? •i got 6x6x1 B) how many numbers would be less then 800(must be 3 digit and divisible by

Math
Explain why the product of any two consecutive natural numbers is even. Prove your conjecture.

Maths
Is this statement true? Give an example to support your answer. "If two numbers are divisible by another number then their difference is also divisible by that number". I think that its like this: 3 and 4 is divisible by 12 then 43=1 so the answer is no?

new math
Tell whether each number is divisible by 2, 3, 4, 5, 8, 9, or 10. Some numbers may be divisible by more than one number. 1.324 2.840 3.2,724 4.81,816 5.7,848

Michael
How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.

Math
Name the subset(s) of real numbers to which the number 2 belongs. Irrational Numbers. Rational Numbers. Integers. Whole Numbers. Natural Numbers.

Math
1) for any three consecutive numbers, what can you say about odd numbers and even numbers? Explain. 2 A)Mirari conjectures that, for any three consecutive numbers, one number would be divisible by 3. Do you think Mirari is correct? Explain. 2 B) Gia claims

Urgent math
Which of following is divisible by 4 for all natural numbers n? (Select all that apply.) please help ?!?!? 5n + 1 − 9 6n − 2 7n + 1 3n + 1 10n − 2

Math! Please Check My Answers
Key: ☺ = My Answer! 2. Write a word phrase for the algebraic expression. 3x  7 A. The difference of three times a number x and seven. B. The difference of seven and three times a number x. C. Three times a number x fewer than seven. ☺ D. The quotient

Math. NEED HELP ASAP.
Im very confused on this. List all the numbers from the given set that are: a. Natural numbers, b. Whole numbers, c. Integers, d. Rational numbers, e. Irrational numbers, f. Real numbers. {3, 2/5, 0, 0.3, ✓3, 5.8, ✓100} list all the natural numbers

Math
There are 30 students in a math class. 12 belongs to the computer club and 8 belongs to the photograph club. three belongs to both. how many belongs to neither???

Easy Math
The number of positive integers that are less than 500 and that are not divisable by 2 or 3 is? There are 250 divisible by 2, 166 divisible by 3 and 83 divisible by both. So 250 + 166  83 = the numbers divisible by 2 or 3, without double counting.

IB HL Math
I need to that if there is better way to prove the following: I am trying to prove that x r = k and k is a multiple of x only when x is prime. I said that if x is nonprime, then: Let a = 6 Let r = 4 6! (6 – 4)! 4! = 3(2) x 5 x 4! (2!) 4! = 15 It is not

Urgent math
Which of following is divisible by 4 for all natural numbers n? (Select all that apply.) please help ?!?!? 5n + 1 − 9 6n − 2 7n + 1 3n + 1 10n − 2

Math for Computer Science
Let n be a natural number. If n is divisible by 9, that is neither a necessary nor sufficient condition for n being divisible by 6, right? Because I'm not sure about the wording of the question asking whether it is either necessary or sufficient, but I

Math  Algebra I
Consider the subsets of R defined as follows: An is the interval (0,1/n) for all natural numbers. Show that: U (union) n=1 to infinity of An = (0,1) Here's what I tried as a proof: Show that (0,1) is a subset of U n=1 to infinity An Take an arbitrary real

Algebra 2
prove or disprove the following statement. Irrational numbers of the form a+√b are closed under multiplication where a and b are natural numbers

math
Find the value of the missing digit that makes the statement true. 214,21_ is divisible by 11 Determine whether the statement is true or false. Why? If a natural number is divisible by 5 and 2, then it must also be divisible by 10.

math
The following conjectures were made by students. Are they true or false? Give a counterexample if possible. Only half of the nonzero even numbers up to 100 are divisible by 4. My answer is that it is true. A number is divisible by 8 if it is divisible by 4

maths helpppppp me asap plz
if the greatest lower limit and the lowest upper limit of the series 1/n, where n belongs to the set of Natural numbers (N), be a and b respectively, then find the value of (a + b). I need help

precalculus
how to prove that this is true for all natural numbers n, using principle of mathematical induction. (3i+2)= 5+8+11+14+...+ (3n+2)=3n^2+7n/2

math
For each number, circle the subset(s) of the real numbers that the number belong to. 26) √49 rational, integers, whole numbers, natural numbers, irrational 27) −√81 rational, integers, whole numbers, natural numbers, irrational 28) √43 rational,

Reiny to Gina (logic)
I saw your reply re my late night solution to your pumpkin question http://www.jiskha.com/display.cgi?id=1224212047 I did indeed make two typing errors, which even though they do not change the actual answer, nevertheless would have caused confusion. I

Math Geometry Proofs
What are some ways to prove that a triange is isoscles? i have to make a two column proof based on a problem. What is the exact problem I need help with my geometry homework. We are doing proofs and i need some help because proofs are really hard!! def.

math
Using the numbers 1 through 9 with no repeats, find a 9 number such that: the first digit is divisible by 1, the first two digits are divisible by 2, the first 3 digits are divisible by 3, and so on until we get to a 9 digit number divisible by 9. You

new math
Tell whether each number is divisible by 2, 3, 4, 5, 8, 9, or 10. Some numbers may be divisible by more than one number. 1.324 2.840 3.2,724 4.81,816 5.7,848

math
to which subsets of real numbers does the number 22 belong? choose all that apply a) whole numbers b) rational numbers c) integers d) irrational numbers e) natural numbers

Maths
Prove that for a,b,c belongs to natural numbers, if a+b+c is divisible by 30 so is a^5+b^5+c^5.

Mathematics
1. 62 is divisible by which of the following numbers? A. 1, 3, 31, 62 B. 1, 2, 3, 31 C. 1, 4, 16, 62 D. 1, 2, 31, 62 2. 45 is divisible by which of the following numbers/ A. 1, 5 8 B. 1, 2, 3 C. 1, 2 ,5 D. 1, 3, 5, 9 3. Which of the following numbers is

Math
Prove that for any natural n the value of the expression (4n+5)^2–9 is divisible by 4.

Algebra
Prove that for any natural value of n the value of the expression: (5n+1)2–(2n–1)2 is divisible by 7

math
Hence show that 5*7^n+3*11^n8 is divisible by 60 for all natural numbers n

math
How do the ideas of divisibility and multiples relate to the study of fractions? Show that 1,078 and 3,315 are relatively prime. What is the shortest length of television cable that could be cut into either a whole number of 18ft pieces or a whole number

Math
1.62 is divible by which of the following numbers? A.1,3,31,62 B.1,2,3,31 C.1,4,16,62 D.1,2,31,62 I PICKED D.  2.108 is divisible by which of the following sets of numbers? A.1,2,3,4,6,9,12,18,27,36,54,108 b.1,2,4,27,54,108

Algebra
23. The ___ axis represents the independent variable. X? 21. Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above

direct methodMath
Prove or disprove the following: If the integer n is divisible by 3 then n^2 is divisible by 3. Use the direct method of proof as outlined in the notes.

Math
Here is the question: If a natural number is divisible by 5 and 2, then it must also be divisible by 10. My answer: false. Is this correct?

Math
Determine whether the statement is true or false. Explain or show why. If a natural number is divisible by 7, then it must also be divisible by 21

Math
1)Find the value of 7+2(52*3^2) 7+2(52*9) 7+2(518) 7+2(13) 7+26 (answer)19 2)Name the sets of numbers to which 457 belongs. (answer)natural,whole,integers,rational,reals

math
List the following subsets of the real numbers in order from least inclusive to most inclusive.(1 point) rational numbers, natural numbers, whole numbers, integers whole numbers, natural numbers, integers, rational numbers natural numbers, whole numbers,

Math
1. What is the 117th odd natural number? 2. What is the greatest threedigit number divisible by 3, 4, 5, and 6? 3. How many even numbers are between 101 and 303? 4 How many even numbers are between 201 and 299? if 52 cards are dealt to 8 people as evenly

Math
The question is this: You know that a number is divisible by 6 if it is divisible by both 3 and 2. So why isn't a number divisible by 8 if it is divisible by both 4 and 2? My answer is this: The only prime factors of 6 are 2 and 3. So, if a number is

maths
The values A,B,C, and [(A/B)+C], are all integers which are divisible by 3. Then, which of the following statements must be true: A is divisible by 9 B is divisible by 9 C is divisible by 9 A and B are both divisible by 9 A,B,and C are all divisible by 9

math
What are the divisibility short cuts that help you out? Odd numbers can only be divided evenly by another odd number. Even numbers can be evenly divided by either odd or even numbers. 2Numbers that end in 0, 2, 4, 6, or 8 are evenly divisible by 2.

Algebra
28. Use the Distributive Property to simplify x(4x^2 + x + 4) Is it 4x^3 + x^2 + 4x? 42. To which set of numbers does 0 not belong? 46. Pi belongs to which group of real numbers? a. Odd numbers b. rational numbers c. irrational numbers C? 48. Can a number

precalculus
proving that the statements are true for all natural numbers 1+2+3+....+n=n(n+1)/2 i don't understand when trying to prove that P(k+1) = 1+2+3+...+k+k(k+1)= 1/2 how do you do this step???

Math/Algebra
if you add one number divisible by n and one number not divisble by n will the result be divisible by n? and.. if you add two numbers not divisible by n will the reult be dvisible by n? explain.

math
The sum of the first 5 natural numbers is 15 or (5)(6)/2. The sum of the first 21 natural numbers is 231=(21)(22)/2, and the sum of the first 30 numbers is 465. Use inductive reasoning to derive the formula for the sum of the first n natural numbers.

algebra
2.Which of the following is an example of closure. a. The equation 4−6=−2 is an example of the whole numbers being closed under subtraction. b. The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition. c. The equation

Math
48,24,6,36,12,54 Which of the following describe this set. A. Numbers that are multiples of 3 B. Numbers that are prime. C. Numbers that are divisible by 6 D. Numbers that are factors of 36 I think its a and c

math
is 504 divisible by 2,4,6,8 is 111 divisible by 3,9 is 3,217 divisible by 3 is 804 divisible by 2,4,6,8

Algebra
To which subset of rel numbers does the number 22 belong? whole numbers rational numbers integers irrational numbers natural numbers I know it's an Integer but I'm not sure of the second answer.

math
please help me!!!!!!!!!!! Identify if the first number is divisible by the second number, and if so, the reason why. Is 26 divisible by 2? A. No B. Yes, because 2 + 6 = 8 and 8 is divisible by 2. C. Yes, because the last digit is 6, which is divisible by

math
find the average of all odd natural numbers , well as that of all the even natural numbers , less than 20 compare the two averages

math
Let N N denote the natural numbers {1,2,3,4,...}. Observe a f that satisfies f(1)=1, f(2n)=f(n), f(2n+1)=f(2n)+1 for all n that are natural numbers. Write a algorithm for f(n).

Permutation and combination
How many natural numbers are there with the property that they can be expressed as sum of cubes of two natural numbers in two different ways.

Calculus
I will be using != for not equal The cancellation law for real numbers is quite obvious: if a,b, and c != 0 are real numbers for which ac = bc then a = b. It is natural to ask if the cancellation law holds for three dimensional vectors. If U x W = V x W, U

math
list all numbers from the given set {9,4/5,0,0.25,/3,9.2,/100} that are a) whole numbers b) natural numbers c) intergers d) rational numbers e) irrational numbers.

Math
Which statement is correct? Explain your choice. If a numbers to divisible by 3 and 6, then it is divisible by 18. If a number is divisible by 2 and 9, then it is divisible by 18.

math
Who proved this statement using deductive reasoning? If a, b, and c are consecutive positive numbers, then a+b+c is divisible by 3.* CARL: Take 4, 5, and 6. 4 + 5 + 6 = 15 which is divisible by 3. So it's true. LAYLA: If we have n, n+1, and n+2, and add

number theory
How do you prove that any palindrome, a number that reads the same backwards and forwards, with an even number of digits is divisible by 11? I know how to show a number is divisible by 11, but how do you prove the above case?

mathsArithmetic progression
Prove that mean of squares of first n natural numbers is (n+1)(2n+1)/6

airthmetic progression
prove that mean of cubes of first n natural numbers is [n(n+1)(n+1)]/4

number theory
The values A,B,C, and [(A/B)+C], are all integers which are divisible by 3. Then, which of the following statements must be true: A is divisible by 9 B is divisible by 9 C is divisible by 9 A and B are both divisible by 9 A,B,and C are all divisible by 9

Math
A binary operation * on the set of real numbers is defined by a*b= a+bab for a,b, c is belongs to R. i) show that the operation is associative. That is, (a*b)*c=a*(b*c) for all a,b,c belongs to R. ii) Find the value of 5*8 and also the value of

Math
Is 2340 divisible by 90 and what is the divisible numbers for my question