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Neporo4naja [7]
3 years ago
6

The line represents the length and height of a skateboard ramp. Find the slope of the ramp.

Mathematics
1 answer:
Goshia [24]3 years ago
6 0
1/1
I hope that this helps!
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A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historic
stellarik [79]

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.

Step-by-step explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

n = 10, p = 0.05

a) None of the LED light bulbs are defective?

This is P(X = 0).

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

P(X = 0) = C_{10,0}*(0.05)^{0}*(0.95)^{10} = 0.5987

There is a 59.87% probability that none of the LED light bulbs are defective.

b) Exactly one of the LED light bulbs is defective?

This is P(X = 1).

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

P(X = 1) = C_{10,1}*(0.05)^{1}*(0.95)^{9} = 0.3151

There is a 31.51% probability that exactly one of the light bulbs is defective.

c) Two or fewer of the LED light bulbs are defective?

This is

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 2) = C_{10,2}*(0.05)^{2}*(0.95)^{8} = 0.0746

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5987 + 0.3151 + 0.0746 0.9884

There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) Three or more of the LED light bulbs are not defective?

Now we use p = 0.95.

Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.

So

P(X \leq 2) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X \leq 2)

In which

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C_{10,0}*(0.95)^{0}*(0.05)^{10}\cong 0

P(X = 1) = C_{10,1}*(0.95)^{1}*(0.05)^{9} \cong 0

P(X = 2) = C_{10,1}*(0.95)^{2}*(0.05)^{8} \cong 0

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0

P(X \geq 3) = 1 - P(X \leq 2) = 1

There is a 100% probability that three or more of the LED light bulbs are not defective.

8 0
3 years ago
Hey guys! 20 points! Please help! A model rocket is launched from a roof into a large field. The path of the rocket can be model
Georgia [21]

Answer:

145.84 meters

Step-by-step explanation:

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What is the relative minimum of the function?
forsale [732]

Answer:

-5

Step-by-step explanation:

Minimum turning point at (1,-5)

6 0
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The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a
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Answer:

There are 2,500 misquitos after 3 days and it takes 158 days to reach 80,000 mosquitos.

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What is 6/100 in simpliest form
FromTheMoon [43]


6 and 100 can both be simplified if you divide them both by 2.
6 divided by 2 is 3.
100 divided by 2 is 50.
So the answer is 3/50. It cannot be simplified any further :)

7 0
3 years ago
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