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Question Number 126765 Answers: 1 Comments: 0

...elementary mathematics... if 13 ∣9^(51) +k+1 , k∈N then k_((min)) =?

$. . . e l e m e n t a r y m a t h e m a t i c s . . .$ $i f 13 ∣ 9^{51} + k + 1, k \in N$ $t h e n k_{(m i n)} = ?$

Question Number 124899 Answers: 0 Comments: 0

Question Number 124409 Answers: 1 Comments: 0

write A′∪ B′ in a disjoint set

$w r i t e A^{'} \cup B^{'} i n a d i s j o i n t s e t$

Question Number 123287 Answers: 1 Comments: 0

... nice calculus ... number theory prove thar ::: 2^(32) +1≡^(641) 0 ✓ notice: without calculator and only with the use of congruence properties..

$. . . n i c e c a l c u l u s . . .$ $n u m b e r t h e o r y$ $p r o v e t h a r :::$ $2^{32} + 1 \overset{641}{\equiv} 0 ✓$ $n o t i c e : w i t h o u t c a l c u l a t o r a n d o n l y$ $w i t h t h e u s e o f c o n g r u e n c e p r o p e r t i e s . .$

Question Number 122436 Answers: 0 Comments: 0

Mean : It is found by adding all the values of the observation and dividing it by the total number of observations. It is denoted by x^ . So, x^ = ((Σ_(i=1) ^n x_i )/n). For an ungrouped frequency distribution, it is x^ = ((Σ_(i = 1) ^n f_i x_i )/(Σ_(i = 1) ^n f_i )) .

$Mean : It is found by adding all the values of the observation and dividing it by the$ $total number of observations . It is denoted by \bar{x} .$ $So, \bar{x} = \frac{\underset{i = 1}{\sum^{n}} x_{i}}{n} . For an ungrouped frequency distribution, it is \bar{x} = \frac{\underset{i = 1}{\sum^{n}} f_{i} x_{i}}{\underset{i = 1}{\sum^{n}} f_{i}} .$

Question Number 122426 Answers: 0 Comments: 0

In an exam 36% of people failed in physics and 49% failed in maths and 15% failed in both subject. If the total number of student that passed physics only is 680 find the total number of students that appeared in the exam .

$In an exam 36 % of people failed in$ $physics and 49 % failed in maths and 15 %$ $failed in both subject . If the total$ $number of student that passed physics$ $only is 680 find the total number of$ $students that appeared in the exam .$

Question Number 121870 Answers: 1 Comments: 0

number theory: m,n ∈ N , (m,n)=1 prove : m^(ϕ(n)) +n^(ϕ(m)) ≡^(mn) 1 ϕ(n)=∣{x∈N∣ x<n , (x,n)=1}∣ .m.n.

$n u m b e r t h e o r y :$ $m, n \in N, (m, n) = 1$ $p r o v e : m^{φ (n)} + n^{φ (m)} \overset{m n}{\equiv} 1$ $φ (n) =∣ {x \in N ∣ x < n, (x, n) = 1} ∣$ $. m . n .$

Question Number 120702 Answers: 0 Comments: 0

Question Number 120044 Answers: 2 Comments: 0

Given a_(n+1) = ((2a_n )/((2n+1)(2n+2))) find a_n .

$G i v e n a_{n + 1} = \frac{2 a_{n}}{(2 n + 1) (2 n + 2)}$ $f i n d a_{n} .$

Question Number 119487 Answers: 2 Comments: 0

find element of set S = { ((x^3 −3x^2 +2)/(2x+1)) ∈ Z for x∈Z }

$f i n d e l e m e n t o f s e t S = {\frac{x^{3} - 3 x^{2} + 2}{2 x + 1} \in Z f o r x \in Z}$

Question Number 119401 Answers: 2 Comments: 0

let d be an application d:R^2 →R_+ d(x,y)=ln(1+((∣x−y∣)/(1+∣x−y∣))) shown that d is a distance on R^2 please help ★especially on triangular inequality

$l e t d b e a n a p p l i c a t i o n$ $d : R^{2} \to R_{+}$ $d (x, y) = l n (1 + \frac{∣ x - y ∣}{1 + ∣ x - y ∣})$ $s h o w n t h a t d i s a d i s t a n c e$ $o n R^{2}$ $p l e a s e h e l p$ $★ e s p e c i a l l y o n t r i a n g u l a r$ $i n e q u a l i t y$

Question Number 117597 Answers: 0 Comments: 1

Let A, B, and C be three sets and X be the set of all elements which belong to exactly two of the sets A,B and C. Prove that X is equal to (A∪B∪C)−[AΔ(BΔC)]

$Let A, B, and C be three sets and X be the set of all$ $elements which belong to exactly two of the sets A, B$ $and C . Prove that X is equal to$ $(A \cup B \cup C) - [A Δ (B Δ C)]$

Question Number 114236 Answers: 2 Comments: 0

70% of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACs and 85% have washing machines. At least what percentage of employees has all four gadgets?

$70 % of the employees in a$ $multinational corporation have VCD$ $players, 75 % have microwave ovens,$ $80 % have ACs and 85 % have washing$ $machines . At least what percentage of$ $employees has all four gadgets ?$

Question Number 114235 Answers: 2 Comments: 0

Let A={(n,2n):n∈N} and B={(2n,3n):n∈N}. Then A∩B is equal to

$Let A = {(n, 2 n) : n \in N} and$ $B = {(2 n, 3 n) : n \in N} . Then A \cap B is$ $equal to$

Question Number 114233 Answers: 1 Comments: 0

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A×B and B×A is

$If two sets A and B are having 99$ $elements in common, then the$ $number of elements common to each$ $of the sets A \times B and B \times A is$

Question Number 114061 Answers: 1 Comments: 0

Question Number 104694 Answers: 0 Comments: 0

Question Number 104544 Answers: 2 Comments: 0

Given a_(n+1) = 5a_n −6a_(n−1) .If a_1 = 10 and a_2 = 26, find a_n ?

$G i v e n a_{n + 1} = 5 a_{n} - 6 a_{n - 1}$ $. I f a_{1} = 10 a n d a_{2} = 26, f i n d a_{n} ?$

Question Number 102357 Answers: 2 Comments: 0

for A={1,2,3,4,5,6,7},compute the number of: (a) Subsets of A. (b) Nonempty subsets of A. (c) proper subsets of A. (d) Non empty proper subset of A. (e) Subsets of A containing three element. (f) Subsets of A containing 1,2. (g) Proper subsets of A containing 1,2. (h) Subset of A with an even number of element. (i) Subset of A with an odd number of element. (j) Subsets of A with an odd number of elements, including the element 3.

$f o r A = {1, 2, 3, 4, 5, 6, 7}, c o m p u t e t h e n u m b e r o f :$ $(a) S u b s e t s o f A .$ $(b) N o n e m p t y s u b s e t s o f A .$ $(c) p r o p e r s u b s e t s o f A .$ $(d) N o n e m p t y p r o p e r s u b s e t o f A .$ $(e) S u b s e t s o f A c o n t a i n i n g t h r e e e l e m e n t .$ $(f) S u b s e t s o f A c o n t a i n i n g 1, 2 .$ $(g) P r o p e r s u b s e t s o f A c o n t a i n i n g 1, 2 .$ $(h) S u b s e t o f A w i t h a n e v e n n u m b e r o f e l e m e n t .$ $(i) S u b s e t o f A w i t h a n o d d n u m b e r o f e l e m e n t .$ $(j) S u b s e t s o f A w i t h a n o d d n u m b e r o f e l e m e n t s, i n c l u d i n g t h e e l e m e n t 3 .$

Question Number 101891 Answers: 3 Comments: 0

if x a integer number , when divided 8 has remainder 5 and divided 5 has remainder 2. find x

$i f x a i n t e g e r n u m b e r, w h e n d i v i d e d 8$ $h a s r e m a i n d e r 5 a n d d i v i d e d 5 h a s r e m a i n d e r$ $2 . f i n d x$

Question Number 98806 Answers: 0 Comments: 1

for a is integer number such that ∣∣x−1∣ −2∣ ≤ a exactly has 2013 solution

$for a is integer number such that$ $∣∣ x - 1 ∣ - 2 ∣ ⩽ a exactly has 2013$ $solution$

Question Number 97438 Answers: 1 Comments: 1

If −3≤x≤4, −2≤y≤5, 4≤z≤10 , find the greatest value of w = z−xy

$If - 3 ⩽ x ⩽ 4, - 2 ⩽ y ⩽ 5, 4 ⩽ z ⩽ 10$ $, find the greatest$ $value of w = z - xy$

Question Number 93950 Answers: 2 Comments: 0

Let ∗ be the binary operation on N given by a∗b=L.C.M. of a and b. Find (i) 5∗7 , 20∗16 (ii) is ∗ communitative? (iii) is ∗ associative? (iv)Find the identity of ∗ in N (v) which elements of N are invertible for the operation ∗?

$L e t * b e t h e b i n a r y o p e r a t i o n o n N$ $g i v e n b y a * b = L . C . M . o f a a n d b . F i n d$ $(i) 5 * 7, 20 * 16 (ii) is * c o m m u n i t a t i v e ?$ $(iii) is * a s s o c i a t i v e ?$ $(iv) F i n d t h e i d e n t i t y o f * i n N$ $(v) which elements of N a r e i n v e r t i b l e$ $f o r t h e o p e r a t i o n * ?$

Question Number 93933 Answers: 0 Comments: 5

Let ∗′ be the binary operation on the set {1,2,3,4,5} defined by a∗′b=H.C.Fof a and b. Is the operation ∗′ same as the operation ∗ defined above? justify your answer.

$L e t *^{'} b e t h e b i n a r y o p e r a t i o n o n t h e s e t {1, 2, 3, 4, 5} d e f i n e d b y a *^{'} b = H . C . F o f a a n d b .$ $I s t h e o p e r a t i o n *^{'} s a m e a s t h e o p e r a t i o n * d e f i n e d a b o v e ? j u s t i f y y o u r a n s w e r .$

Question Number 93567 Answers: 1 Comments: 1

Given that A={0,1,3,5} B={1,2,4,7} and C={1,2,3,5,8} prove that (i) (A∩B)∩C = A∩(B∩C) (ii) (A∪B)∪C = A∪(B∪C) (iii) (A∪B)∩C = (A∪C)∪(B∩C) (iv) (A∩C)∪B = (A∪B)∩(C∪B)

$G i v e n t h a t A = {0, 1, 3, 5} B = {1, 2, 4, 7} a n d C = {1, 2, 3, 5, 8} p r o v e t h a t$ $(i) (A \cap B) \cap C = A \cap (B \cap C)$ $(ii) (A \cup B) \cup C = A \cup (B \cup C)$ $(iii) (A \cup B) \cap C = (A \cup C) \cup (B \cap C)$ $(iv) (A \cap C) \cup B = (A \cup B) \cap (C \cup B)$

Question Number 88761 Answers: 0 Comments: 4

if a_n =((n!)/(n^n e^(−n) (√(2πn)))) and b_n =(((2n)!(√n))/(4^n (n!)^2 )) lim_(n→∞) a_n =1 find lim_(n→∞) b_n =?

$i f a_{n} = \frac{n!}{n^{n} e^{- n} \sqrt{2 π n}}$ $a n d b_{n} = \frac{(2 n)! \sqrt{n}}{4^{n} {(n!)}^{2}}$ $Double subscripts: use braces to clarify$ $Double subscripts: use braces to clarify$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7

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