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2 years ago

What is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...

Mathematics

2 answers:

serg [7]2 years ago

4 0

Answer:

$a_{n}$ = 5 $(2)^{n-1}$

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2

this indicates the sequence is geometric with explicit formula

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = 2 , then

$a_{n}$ = 5 $(2)^{n-1}$

Tcecarenko [31]2 years ago

3 0

Step-by-step explanation:

as we see in the sequence, each term is twice of the previous term.

we mark the Nth as a(N), then:

a(N)=2a(N-1)

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3 years ago

Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Exp

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Answer:

It is a case of classical probability.

Step-by-step explanation:

Since we are selecting a number between 1 and 100 randomly which is divisible by 14 the only favorable cases are 14,28,42,56,70,84,98 which are 7 cases out of 100 total numbers thus the required probability becomes

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Step-by-step explanation:

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2 years ago

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3 years ago

The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 18, meaning that among

jeyben [28]

Answer:

(a) The value of P (None) is 0.062.

(b) The value of P(at least one) is 0.938.

(d) The event is not unusual.

Step-by-step explanation:

Let X = number of households watching the show.

The probability of the random variable x is, P (X) = p = 0.18.

The sample selected for the survey is of size, n = 14

The random variable X follows a Binomial distribution with parameter n = 14 and p = 0.18.

The probability of a Binomial distribution is computed using the formula:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...$

(a)

Compute the probability that none of the households are tuned to CSI: Shoboygan as follows:

$P(X=0)={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}=1\times1\times0.06214=0.062$

Thus, the value of P (None) is 0.062.

(b)

Compute the probability that at least one household is tuned to CSI: Shoboygan as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-0.062\\=0.938$

Thus, the value of P(at least one) is 0.938.

(c)

Compute the probability that at most one household is tuned to CSI: Shoboygan as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

$={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}+{14\choose 1}(0.18)^{1}(1-0.18)^{14-1}\\=0.062+0.191\\=0.253$

Thus, the value of P(at most one) is 0.253.

(d)

An event that has a very low probability of occurrence is known as an unusual event.

The probability of the event "at most one household is tuned to CSI: Shoboygan" is 0.253.

This probability value is not low.

Hence, the event is not unusual.

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3 years ago