Let a,n be integers with 2

Q: A set A has measure zero iff for any ε > 0, A can be covered by intervals whose total length is less…

A:

Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: State and prove fatau's lemma.

A: statement of fatau's lemma :- Let fn be a sequence of non-negative measurable function . and fn→f…

Q: is divengent 2) Show that the harmoni series

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Q: Use Fermat's Theorem to find a number x between 0 and 28 with x 85 congruent to 6 modulo 29. (You…

A: as given  x85≅6mod 29   ...i as we known 29 is a prime number  by fermat's little theorem if p is a…

Q: Use Euler's Theorem to find a number x between 0 and 28 with x85congruent to 6 modulo 35. (You…

A: Here finds the value of x for which: x85≡6mod35 and x lies between 0​  to 28

Q: Is given in th

A: The most repeating games used by the researchers that can be played quickly. It is discovered that…

Q: This question concerns bit strings of length five. The weight of a bit string is the number of l's…

A: Given: The weight of a bit string is the number of 1's the bit string contains. To find: The least…

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: If the interval [2,7] is partitioned into n= 8 subintervals of equal length, what is Ax? Ax = |…

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Q: prove that tan(ix)= itanh(x)

A: Here we prove thattanix=i tan hx

Q: Use algebra to find the largest possible value of 8 or small- est possible value of N that makes…

A: 23. This equation comes from the ε,δ definition of the limit. As x→2 the function 3x-1→5. So for all…

Q: If the interval [4,9] is partitioned into n = 5 subintervals of equal length, what is Ax? Ax = (Type…

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Q: Consider the functi on f(z) = 2 -a with lal >1 %3D 1- az Show that if 121 >1, the lf(Z)< 1

A: Given the function f(z)=z-a1-a¯z with |a|&gt;1.To prove that if |z|&gt;1, then |f(z)|&lt;1

Q: Suppose a, n E Z and 0 < a< n. Prove that ()- (":")- (:-) n - 1 %3D + a a а- 1 in two different…

A: Given a,n∈ℤ such that 0&lt;a&lt;n. (1) Consider:…

Q: Table below show the heights of the 5 starter players of 5 basketball teams in a competition. Every…

A: Introduction: Different teams may use different measures to determine whether they are the tallest…

Q: or an integer n>=3, an n-gon is an n-sided polygon. (example, a 3-gon is a triangle, 4-gon is a…

A: To prove: the sum of the interior anles of every polygon with n sides is n-2180° Now we shall take a…

Q: Assume that (an) and (bn) Cauchy sequences. Set cn = |an – bn|. Prove that (cn) is Cauchy. are

A: Given: an and bn are Cauchy sequences. cn=an-bn To prove: cn is a Cauchy sequence.

Q: Let n, m, a, b be positive integers. motl Lof oontredietion u th

A: Given, n, m, a, b be positive integers. To prove that…

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: #3. Let n be an integer with nz1 and Let b, bz . bn be ... positive real numbers, not all egual,…

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Q: 6. Prove that ER, # 0.

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Q: 2. Prove that the Cartesian product N Nis countable

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Q: Determine all positive number replacements​ (less than the​ modulus) for the question mark that make…

A: Let the required number be x , where x&lt;1 .

Q: 2 Reciangle AlCD with verlices A(-3,01,2C2.0), and tor 粉

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Q: Least residue of 45^37 mod 19 when using Fermats Little Theorem

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Q: What is the maximum number of people you can invite so that at most 3 guests are born same month?…

A: The Pigeonhole Principle: If n + 1 objects are placed into n boxes, then some box contains at least…

Q: If f is.q field a hom- saplar monic polphomial in tay can be factored as q, product of monie primes…

A: Any non-zero non-unit element as a product of primes up to order and up to units. Now  If a≠0 and…

Q: prove that integer V intgers is an

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Q: Prove that intersect on of two sees Sets Sets Set? lonve ond hence ony number of lonved. what ebout…

A: To show:  Intersection of two convex sets is convex   Let A, B be two convex sets  We need to show…

Q: 2. Show that (i) tan 48° tan 23° tan 42° tan67° =1

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Q: 35. A o-field cannot be countably infinite. Its cardina least that of the continuum.

A: Let F be an infinite sigma field.

Q: Prove that (-1+ iB)" + (-1- i3)" has either the velue 2t! or the value if a B any integer (positive,…

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Q: The Extended Euclidean Algorithm allows us to efficiently compute inverses in Z∗n (and also in…

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Q: Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many…

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Q: Prove using weak induction that: For any convex polygon with n sides (n ≥3), any triangulation…

A: now if we look at this procedure This is strong induction. Let Φ(n) be the statement that all…

Q: Find th: units digitof 3" ++ 11* ", whe re e and n: arc: nan-npitve intrgers

A: To solve this question we need to find out unit digit of each term and then add these unit digits to…

Q: Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5).  Give 2 examples to…

A: Given, x,y∈ℤ and x≡1mod 5, y≡2mod 5

Q: se Euler's Theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 35. (You…

A: By using the fernet's theorem: If a and n are co prime. That is (a,n)=1 then aϕ(n)≡1modn For n=35…

Q: [Hint: It suffices to show that the numbe 11. Verify that 0, 1, 2, 2², 2³, . , 2° form a complete…

A:

Q: Use inductive reasoning to predict the nest ine in the sequence of computations. Then use a…

A: We observe that the sequence is the product of two numbers where the 1st number is multiple of 11…

Q: Find the first 4 terms of Toaylor Polyuocuial generated by fCx)= xlnx at a=2.

A: We find first four terms of Taylor polynomial generated by f(x)=xln(x) at a=2.

Q: 7) Show that if a, > 0, and Lim na, +0, then the series aj + az + az + a4 + diverges.,

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Q: Partition (Z/19Z)* into equivalence classes determined by the identi- fication of elements of the…

A: According to the given information, it is required to determine the primitive roots modulo 19.

Q: If the interval [3,10] is partitioned into n = 8 subintervals of equal length, what is Ax? Ax =…

A:

Q: Prove that 1 tan 7 1 + tan tan 13 9.

A: Given : tan-117+tan-1113 = tan-129

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.