3. Every year, a tree produces three more fruits than it did the previous year. If it bore 12 fruits in 1985, how many fruits did the tree bear in total from 1985 until 1996? Express the total number of fruits using sigma notation.

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: 1. A population of fruit flies quadruples every month. How many fruit flies will there be after 8…

A: Given query is to find the population of flies after 8 months.

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: Certain bacteria cells are being observed in an experiment. The population triples in 1 hour.  If at…

A:

Q: 61,000 people died in the worst flu season of the past decade.Covid 19 has killed eight times that…

A: Number of people died during Covid 19  is eight time the number of people died during worst flu.

Q: Find the exponential generating function for the number of partitions of [n] in which each block has…

A:

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: Use sigma notation to write the sum.

A:

Q: a) Find the population after 7 years. (Round to the nearest integer as nee

A:

Q: The fraction can be represented by the repeating decimal 0. 142857. What is the 41st digit after the…

A:

Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

Q: Suppose each license plate in a certain state has three letters followed by three digits. The…

A: * License plate must have       3 letters and 3 digits ; repetitions allowed.Also , letters H and L…

Q: What is the big-omega notation for 1* +2*++*?

A:

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: 17. How many significant figures are there in (a) 0.0000303 and (b) 6.201 x 10?

A: We have to find the significant figures in the given numbers.

Q: 2. Suppose that the number of bacteria in a colony triple every hour. a) Set up a recurrence…

A:

Q: In(n)

A:

Q: In n

A: Given as, an =Innn3

Q: FIND THE SMALLEST n So THAT I

A: In this question, we have to find n for given |Rn|<0.0001.

Q: (nt) n=1

A: we have to find the sum

Q: Find the proportion of primes p in the interval from 10^12 and 10^12 + 1000 such that p-1 is B= 105…

A:

Q: Express the repeating decimal 1.2345345345 . . . as a  fraction.

A: we have to express the repeating decimal 1.2345345345 . . . as a  fraction.

Q: 5. A certain bacteria triples every 2 hours. If at 9:00 am there are initially 1000 bacteria, how…

A:

Q: A farmer has a crop of 2,000 orange trees at the beginning of this year. Each year, the farmer plans…

A: Given,         A farmer has a crop of 2000 orange trees at the beginning of this year. Each year,…

Q: When the movie The Dark Knight was released in 2008, a news report stated that 62% of the people who…

A: Given,

Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

Q: An object with negligible air resistance is dropped from the top of theWillis Tower in Chicago at a…

A: In this question we will use basic of algebra. We will simply write an expression of equations of…

Q: a.For the 2019 Comrades marathon, 17268 men and 4357 women entered, 15835 men and 3982 women started…

A: As per bartleby guidelines for more than one question, only 1st one is to be answered. Please upload…

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: Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their…

A:

Q: 16. Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: Take integer and add them with his reciprocal Diifferenciate and get

Q: AND THIS sum !

A: Given : ∑N =1∞2NN+2

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: 3. A city has been found to have a population that triples every four years. If the city's…

A: Given that that city has been found to have a population that triples every four years and the…

Q: (-5)"-1 Find the sum of the series 6" n=0 Maximum number of characters (including HTML tags added by…

A: Given: ∑n=0∞(-5)n-16n Simplify the expression. ∑n=0∞(-5)n-16n=∑n=0∞(-5)n-1·6-n=-∑n=0∞-56n5…

Q: b) Suppose that the number of bacteria in a colony doubles every hour. i) Set up a recurrence…

A: (i) Given that number of bacteria  doubles every hour, the recurrence relation for the number of…

Q: Use sigma notation to write the sum. [(+) 2 + 5 4 6. + 5 + 5

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: Give a partition of I = [-1, 1] with 5 partition points such that the lengths of the subintervals…

A: Solution :-

Q: n that includes all terms up to

A: The initial value problem is , w''+7xw'-w=0. It is given that w0=6, w'0=0. w''+7xw'-w=0. To find the…

Q: Express the given repeating decimal as a quotient of integers. If​ possible, reduce to lowest terms.…

A:

Q: Define β1 stands for?

A: β1 is mainly used in linear regression.  The linear regression is defined as the mathematical linear…

Q: Use generating functions to determine the number of 9-digit sequences of the digits 1,2,3,4,5,and 6…

A: We need to find ,  number of 9-digit sequences of the digits 1,2,3,4,5,and 6 in which each even…

Q: An object thrown upward from the ground falls to the ground after k seconds. Which of the following…

A:

Q: Use sigma notation to write the sum. (e) - e)-- )-E) 2n 2n

A: To solve this question we have to see carefully which term or terms is/are repeating. Then in sigma…

Q: Determine which reduced fractions have a repeating decimal of the form 0.aaa . . . , where a = 0, 1,…

A:

Q: The five-day flu is a rare disease. If contracted, on day one of the disease the infected person…

A: we are allowed to solve 3 subparts only  (a) On the first day, the patient sneeze once i.e. 1 time…

Q: Determine whether the sequence {5n−7 / 3n+4} is increasing, decreasing, or neither.

A: