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2 years ago

Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.

Mathematics

1 answer:

Goshia [24]2 years ago

4 0

Answer:

$\sf 2^{(n+1)}$

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

$\sf \boxed{\bf t_n=ar^{(n-1)}}$

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

a = 4

r = 8 ÷4 = 2

$\sf t_n =4*2^{(n-1)}$

$\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n$

$\sf = 2^{(n+1)}$

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The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70% of pr

Ne4ueva [31]

Answer:

it will take a programmer about 16.67 times to work before they are fired

Step-by-step explanation:

From the information given;

The transistion matrix for this study can be computed as:

P M X

P 0.7 0.2 0.1

M 0 0.95 0.05

X 0 0 1

where;

The probability that the programmer remains a programmer = $(P *P)$

The probability that the programmer turns out to be a manager = $(P*M)$

The probability that the programmer is being fired = $(P*X)$

Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;

$y(P)=1+0.7y(P)+0.2y(M)$

$y(M)=1+ 0.95y(M).$

$0.05y(M)=1$

y(M) = $\dfrac{1}{0.05}$

y(M) =20

y(P)=1+0.7y(P)+0.2y(M)

y(P) - 0.7y(P) = 1 + 0.2y(M)

0.3y(P) = 1 + 0.2(20)=1+4

0.3y(P) = 1 + 4

0.3y(P) = 5

$y(P)=\dfrac{5}{0.3}$

$y(P)=16.67$

Therefore, it will take a programmer about 16.67 times to work before they are fired

8 0

3 years ago

I’ll mark as BRANLIEST!!<br><br> Please help me!!<br><br> 40 POINTS!!!

SCORPION-xisa [38]

Step-by-step explanation:

Notice that B = {1, 3, 5, 7} and C = {0, 2, 4, 6, 8, 10}.

A U B = {1, 3, 5, 7}.

B ∩ C = { }.

A U C = {0, 1, 2, 4, 5, 6, 7, 8, 10}.

8 0

3 years ago

Find the missing character (?)

4vir4ik [10]

The answer is 7, your welcome :).

6 0

4 years ago

David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that

balandron [24]

Using the hypergeometric distribution, it is found that there is a 0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.

The people are chosen without replacement from the sample, hence the <em>hypergeometric distribution </em>is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

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

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 18 people, hence $N = 18$ .

2 people will be chosen, hence $n = 2$ .

David and Valerie corresponds to 2 people, hence $k = 2$ .

The probability that both get picked is P(X = 2), hence:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,18,2,2) = \frac{C_{2,2}C_{16,0}}{C_{18,2}} = 0.0065$

0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.

You can learn more about the hypergeometric distribution at brainly.com/question/25783392

7 0

2 years ago

Can anyone help me with this problem

8_murik_8 [283]

They way I would do it other than with a calculator would be
27 x (90 - 0.5) which is the same as 27 x 89.5
=> 27 x 90 - 27 x 0.5
27 x 90 is (3 x 9) x 90 or 3 x 9 x 90
9 x 90 = 810
3 x 810 = 2430
Then subtract 27 x 0.5, or 27 / 2
2430 - 27 / 2
=> 2430 - 13.5
= 2416.5

Final answer:
2416.5
Hope I helped :)

6 0

3 years ago