Mrs. Hill asked her students to express the sum 1+ 3+ 5+ 7+9+...+ 39 using sigma notation. Four different student answers were given. Which student answer is correct? Select one: 37 O a Zk+2) k--1 40 Ob. E«- 1) k-2 39 E(2k – 1) k-1 20 O d. 2(2k - 1) k-1

Q: Sam is laying out patio stones in a triangular pattern. The first row has 2 stones and each row has…

A: Here,  Row 1 has 2 stones Row 2 has 2+2=2(2)=4 stones Row 3 has 2+2+2=2(3)=6 stones . . .

Q: We can use sigma notation to rewrite the sum 4 + 7+ 10 + 13 + + 31 as: ... 4 +7+ 10 + 13 + ..+ 31 =…

A:

Q: 1), n = 1, 2, . .

A: In this question, the concept of mathematical induction is applied. Mathematical Induction Inductive…

Q: Prove that n2 > 2n + 1 for n ≥ 3. Show that the formula is true for n = 3 and then use step 2 of…

A: To show that n2 > 2n + 1 for n ≥ 3 using mathematical induction.

Q: 26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must…

A:

Q: solve 5.3 (using k(pi-k)/2) and setting k =pi/2 or by your own methods if you have easier ones

A: It is known to us that

Q: 62. Prove part (b) of Theorem 4.4 in the case when n is odd: If n(n+1) n is a positive odd integer,…

A: ∑k=1nk=n(n+1)2 , n is odd integer

Q: 1. Compute the value of (), for n > 3.

A: Formula: nr=n!r!n-r!

Q: 5.2.8 suppose that a store offers gift certificates and denominations of $25 and $40. Determine the…

A: The given denominations are $25 and $40.Here, the given denominations are multiples of 5.The amounts…

Q: ity by 11 by alternately adding and subtracti left, beginning with the units digit-that is, units…

A:

Q: S = CMN2 for N2

A:

Q: (b) Show that k-1 (k+1) n n+1 for every n ≥ 1.

A:

Q: Prove by mathematical Induction 1(2)+2(3)+3(4)+...+n(n+1)=n(n+1)(n+2)/3

A: We will prove the given statement using mathematical induction method.

Q: Show that 1/n - 1/(n+2)= 2/(n(n+2))

A:

Q: The formula for calculating the sum of all natural integers from 1 to n is well-known: n² Sn…

A: This question is related to principal of Mathematical induction . solve in step 2.

Q: You brush your teeth very, very carefully in the morning at 6am leaving only 1000 bacteria on your…

A: We will find a sequence for number of bacteria .

Q: The series expression for 1 1.4. 1.4.7 1:4.7.10 2 8 32 128 (n+ 1)! Σ n=2 (n- 2)! (–1)^+1(1 -4·7- (3n…

A:

Q: a population, N = 10,000, μ = 122, and σ = 15. Find to 2 decimal places the z value for for n = 25…

A: Given: Population mean (μ) = 122 Population standard deviation (σ) = 1 5 Sample size (n) = 25 x¯=121

Q: 4. Let, a, = 1, az = 2, b, = 0, b2 = 1, for n 2 3, an = 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 express…

A:

Q: In a sample of 30 cats from a population with a probability of 0.19 of having a coat of fur with…

A:

Q: 4. Find the largest value of n such that 2"|16!.

A:

Q: Prove 1 0, Ø ! n n=1

A:

Q: 2) (n² – n – 29) ÷ (n – 6) 4) (k² – 7k + 10) ÷ (k – 1) tv

A:

Q: * if the o is not known and (n< 30) can be used z O

A: Which one is the correct choice

Q: 7 Prove by induction, showing all of your algebra steps: (-1) + 4 + (-9) +.….. + (-1)"n² = (-1)°n(n…

A: 7 We have to prove that −1+4+−9+....+−1nn2=−1nnn+12 by principal of induction method. First check…

Q: Show that 2n+1≤2^n  for all n≥3.

A:

Q: Within the interval (0,1)we randomly choose two numbers: x and y . Determine the probability that…

A: The problem can be solved using the concept of basic probability.

Q: Use any method to deter (a) 13 The series 8.

A:

Q: The equation 2 +4+6+ 8+ • · .+ 2n = n (n + 1), n > 1,n an integer can be proven by mathematical…

A:

Q: Suppose that 2% of a population carries antibodies to a virus. For a research project, you need 8…

A: Given that 2% of the population carries antibodies to a virus. Hence the probability that a person…

Q: In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order…

A: Introduction: It is understood that a player wins the jackpot if they choose the 5 distinct number…

Q: 18. Show that Σkind(k)³ = (Σk|n d(k))² for all positive integer n.

A:

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: Find the sum of the first five natural even numbers using sigma notation.

A: We have to find sun of first 5 even natural numbers.

Q: (a) A team of 5 debaters of IUB is to be chosen from a section where we have 6 male and 4 female…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: The probability that an archer hits the target is p = 0.9, so the probability that he misses the…

A: Here's it follows binomial distribution with trial 6 and probability of success 0.9 , probability of…

Q: Sigma(n=1 to n= infinity) 5* (2n-

A: We have to solve given problem:

Q: -)) In how many days does 7 masters paint the wall painted by 5 masters in 14 days

A:

Q: A man has seven keys on a key ring, one of which fits the door he wants to unlock. He randomly…

A:

Q: A second-stage smog alert has been called in a certain area of Los Angeles County in which there are…

A: Introduction: Denote the random variable X as the number of firms violating at least one of the…

Q: A sequence of numbers co, ¤1, X2, .. . is such that xo = 4 and, 6. %3D for each n > 1, 1. In 3n-1+2.…

A:

Q: 6.2.2 Show that if there are 30 students in the class, and at least 2 have a last name that begin…

A: Consider the provided statement that there are 30 students in a class then at least two have last…

Q: Using mathematical Induction Principle Show n2<n! ; n≥4

A: Firstly show the result holds for base case Assume the result holds for n=k and show the result also…

Q: Find σ(n) if n = 2^k-1 (2^k - 3) where 2^k - 3 is prime

A:

Q: tion 4: Prove the following by using the principle of mathematical induction, n is a [3] positive…

A:

Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: Serial numbers for a product are made using 3 letters followed by 2 numbers. If the letters are…

A:

Q: nt 2 GIVEN: *In ( 1+) hai (-1)" (n +2) 2n+1(n + 1) 4. Compute the exact value of )` n=0

A:

Q: for n greater or equal to 1  proove that 2+4+6+...+2n=n^2+n by using mathematical induction

A:

Q: Show that...

A: To show: That n0=nn for n≥0. Concept used: The combination are shown below: Crn=n!r!n-r!…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.