If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9, find the probabilities that among 20 such lights a. Exactly 18 will have a useful life of at least 800 hours; b. At least 15 will have a useful life of at least 800 hours; c. At least 2 will not have a useful life of at least 800 hours.

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: A = 6 -2 -2 10 -3 5 1 ---3-0 C=0-2 a = 1, b = [3 08]. -10 1 . B 5 2 11 9 4 4 7 0 0 11

A: We have to solve given Questions.

Q: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: Find L{1}ℒ{1}.

A:

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: Simplify.2 Express 0(3n° – 2n² + n) n) as:

A: Given that O(3n^3 - 2n^2 + n)

Q: (5V3)2

A: Explanation of the solution is given below...

Q: 7/2 + 3 4/6

A:

Q: expand (a-b)7

A: The solution is given in the next step.

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: 9/12+3/24

A:

Q: 3/8+5/24

A: The given expression is 3/8 + 5/24.Simplify the given expression as follows.

Q: 20/5+5+2*8

A: Consider the given expression

Q: Reduce the following to the lowest terms. Show how to calculate the greatest common divisor by the…

A: The given fraction number is,Here we can write,As we can see the number 4 can be canceled out.This…

Q: factors of 20 that add up to 9

A:

Q: coefficient of variaton for given populaion   5,8,9,11,15,16,17,19

A:

Q: 1/4 +5/4

A: Solution: The objective is to find the value of the given expression

Q: 42. The term that does not contain x in the expansion of 8x +

A:

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

A:

Q: 5 7/12 + 1 3/4 + 4 1/2

A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

Q: 1/5 + 1/10 + 1/15

A: Sum of numbers

Q: 9 5/12 - 3 2/3 =

A: Case 1: Let the given number be in mixed fraction notation.

Q: -3n in

A:

Q: 6 3/20 - 6 3/8

A:

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

A:

Q: 2/5 +7/12

A: Please see the answer below.

Q: 22 7/8 - 7=

A: Given,

Q: 3 3/4 + 2 7/28

A:

Q: mplify. (76)2

A:

Q: 1/20+1/10+1/4

A:

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.