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3 years ago

What is the next term of the following geometric sequence:

Mathematics

1 answer:

LenKa [72]3 years ago

4 0

Answer:

Step-by-step explanation:

Each term has been multiplied by 2/5.

-1/2 * 2/5 = -2/10=-1/5

-1/5 * 2/5 = -2/25

-2/25 * 2/5 = -4/125

-4/125 * 2/5 = -8/625

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Based on past experience, the main printer in a university computer centre is operating properly 90% of the time. Suppose inspec

yaroslaw [1]

Answer:

a) 38.74% probability that the main printer is operating properly for exactly 9 inspections.

b) Approximately 100% probability that the main printer is operating properly for at least 3 inspections.

c) The expected number of inspections in which the main printer is operating properly is 9.

Step-by-step explanation:

For each inspection, there are only two possible outcomes. Either it is operating correctly, or it is not. The probability of the printer operating correctly for an inspection is independent of any other inspection, which means that the binomial probability distribution is used 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.

Based on past experience, the main printer in a university computer centre is operating properly 90% of the time.

This means that $p = 0.9$

Suppose inspections are made at 10 randomly selected times.

This means that $n = 10$

A) What is the probability that the main printer is operating properly for exactly 9 inspections.

This is $P(X = 9)$ . So

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

$P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874$

38.74% probability that the main printer is operating properly for exactly 9 inspections.

B) What is the probability that the main printer is operating properly for at least 3 inspections?

This is:

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{10,0}.(0.9)^{0}.(0.1)^{10} \approx 0$

$P(X = 1) = C_{10,1}.(0.9)^{1}.(0.1)^{9} \approx 0$

$P(X = 2) = C_{10,2}.(0.9)^{2}.(0.1)^{8} \approx 0$

Thus:

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0 = 0$

Then:

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0 = 1$

Approximately 100% probability that the main printer is operating properly for at least 3 inspections.

C) What is the expected number of inspections in which the main printer is operating properly?

The expected value for the binomial distribution is given by:

$E(X) = np$

In this question:

$E(X) = 10(0.9) = 9$

3 0

3 years ago

What is equal to 20/40?

vagabundo [1.1K]

Answer:

1/2 is equal to 20/40

that is the answer

7 0

3 years ago

Read 2 more answers

A car drives at a speed of 34 2/3 mph. How many miles will the car travel in:<br> 40 min?

Ierofanga [76]

40 minutes is not a full hour so you need to convert this to hours

40 minutes / 60 minutes = 2/3 of an hour

So a car driving at the rate of 34 2/3 mph will go

34 2/3 * 2/3 = Miles in 40 minutes

40 * (4/9) = ?or

160/9 = ? or

17 7/9 Miles

7 0

3 years ago

On a scale drawing, the scale is 1/2 inch = 1 foot. What are the dimentions on the scale drawing of a room that is 22 feet by 17

Finger [1]

It would be 44 inch by 34 inch