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Goryan [66]
3 years ago
10

PLEASE HELP ME WITH THESE 2 QUESTIONS YOU GUYS, I AM TRYING TO PASS MATH CLASS. PLEASE. please. I AM GIVING 30 PTS FOR THIS. PLE

ASE.
1. Write the recursive formula and the explicit formula for the sequence {-15,-7,1,9, 17,...}. Show all work.

2. In a paragraph, write which formula, recursive or explicit, is easiest for you to use when finding the 10th term in a sequence. Explain your reasoning in complete sentences.
Mathematics
2 answers:
11Alexandr11 [23.1K]3 years ago
7 0

<u>Recursive formula</u>: a_{n} = a_{n-1} + d  ; where a_{n-1} is the previous term, d is the difference, n is the term.

a_{n} = a_{n-1} + 8

<u>Explicit formula</u>: a_{n} = a₁ + d(n - 1)   ; where a₁ is the first term, d is the difference, n is the term.

a_{n} = -15 + 8(n - 1)

      = -15 + 8n - 8

      = 8n - 23

********************************************************************************************

<u>Using Recursive formula</u>: a₁₀ = a₉ + 8

a₁ = -15

a₂ = -15 + 8 = -7

a₃ = -7 + 8 + 1

a₄ = 1 + 8 = 9

a₅ = 9 + 8 = 17

a₆ = 17 + 8 = 25

a₇ = 25 + 8 = 33

a₈ = 33 + 8 = 41

a₉ = 41 + 8 = 49

a₁₀ = 49 + 8 = 57

<u>Using Explicit formula</u>:  a₁₀ = 8(10) - 23

a₁₀ = 80 - 23

a₁₀ = 57

Bad White [126]3 years ago
4 0

Explicit Formula

Just in case you don't know what this is, the explicit formula is the formula that solves for any term in the series without necessarily knowing what came before the term you are solving.

<em><u>Givens</u></em>

d = t_(n + 1) - t_n  You can take any term and the next term for this part of the formula

d = t_3 - t_2

t_3 = 1

t_2 = -7

d = 1 - - 7 = 8

a = -15

<em><u>Formula</u></em>

t_n = a + (n - 1)*d

t_n = -15 + (n - 1)*8

For example find the 5th term.

t_5 = - 15 + (5 - 1)*8

t_5 = - 15 + 4 *8

t_5 = -15 + 32

t_5 = 17  Which is what you have.

Recursive Formula

Computers really like this formula. They use it in what is called a subroutine and they pass values from one part of the program to a subroutine which evaluates the given and sends the result back. I'm telling you all this so you see why you are doing it. The disadvantage of it for humans is that you must know the preceding term to use the recursive formula.  

<em><u>Formula</u></em>

t_n = t_(n - 1) + d

<em><u>Example</u></em>

t_6 = t_(6 - 1) + d

t_6 = t_5 + 8

t_6 = 17 + 8

t_6 = 25

You can check this by using the explicit formula.

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16. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours
Reika [66]

Answer:

a) 23.11% probability of making exactly four sales.

b) 1.38% probability of making no sales.

c) 16.78% probability of making exactly two sales.

d) The mean number of sales in the two-hour period is 3.6.

Step-by-step explanation:

For each phone call, there are only two possible outcomes. Either a sale is made, or it is not. The probability of a sale being made in a call is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:

Six calls per hour, 2 hours. So

n = 2*6 = 12

Sale on 30% of these calls, so p = 0.3

a. The probability of making exactly four sales.

This is P(X = 4).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{12,4}.(0.3)^{4}.(0.7)^{8} = 0.2311

23.11% probability of making exactly four sales.

b. The probability of making no sales.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138

1.38% probability of making no sales.

c. The probability of making exactly two sales.

This is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678

16.78% probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

The mean of the binomia distribution is

E(X) = np

So

E(X) = 12*0.3 = 3.6

The mean number of sales in the two-hour period is 3.6.

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3 years ago
Miguel wants to buy a condominium. He has the choice of buying it now or renting it with the option to buy at the end of 3 years
kolbaska11 [484]
Total amount paid if he bought = 6000 + 726(12 x 3) = 6000 + 726(36) = 6000 + 26,136 = 32,136
Total amount paid if he rents = 2000 + 37P, where P is the monthly rent

For renting to be cheaper
2000 + 37P < 32,136
37P < 32136 - 2000 = 30136
P < 30136 / 37 = 814.49

Therefore, the maximum rent he could pay is $814
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There are 80 people waiting to tour the science museum. The tour guide takes 4 groups of 16 people each. The remaining people wi
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Answer:

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Step-by-step explanation:

Given that :

Number of people to tour = 80

Number per group = 16

Number of groups = 4

Total number of people who make up the entire groups :

Number per group * number of groups

16 * 4 = 64

The number of people in the last tour group :

80 - 64

= 16 people

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The degree of the polynomial is 7
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