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3 years ago

Question is provided in the image attached. 25 points!

Mathematics

1 answer:

earnstyle [38]3 years ago

7 0

Hey!

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Find the zero term:

Plug in 0 for n.

a = 8 + 3(0 - 1)

a = 8 + 3(-1)

a = 8 + (-3)

a = 5

Answer: 5

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Find the first term:

Plug in 1 for n.

a = 8 + 3(1 - 1)

a = 8 + 3(0)

a = 8 + 0

a = 8

Answer: 8

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Find the 40th term:

Plug in 40 for n.

a = 8 + 3(40 - 1)

a = 8 + 3(39)

a = 8 + 117

a = 125

Answer: 125

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Hope This Helped! Good Luck!

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Answer:

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3 years ago

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The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 500 hours. If an assembly

skelet666 [1.2K]

Answer:

A) probability of failure in next 100 hours given that it has been tested for 500 hours without failure is 0.181

B) probability that exactly two have the metabolic defect is 0.03

Step-by-step explanation:

Part A)

Let X be a exponentially random variable with mean = μ = 500 hrs

For exponential distribution:

$p.d.f = f(x) = \lambda e^{-\lambda x}\\c.d.f = F(x) = 1 - e^{-\lambda x}\\x\geq 0$

λ = 1/μ

λ = 0.002

We have to find the probability of failure in the next 100 hours given that assembly has been tested for 500 hours without a failure.

Using memory less property of exponential distribution:

$P(X500) = P (X$

using

$F(x) = 1 - e^{-\lambda x}\\ \lambda =.002\\x=100\\F(x) = 1- e^{-(.002)(100)}\\F(x) = 1-.8187\\F(x) = 0.181$

Chances of occurrence of metabolic defect = 5%

P(C) = .05

No. of randomly selected infants = n =6

We have to find the probability that exactly two have the metabolic defect

⇒x = 2

Using binomial probability density function:

P = $P=\left[\begin{array}{ccc}n\\x\end{array}\right] p^{x} (1-p) ^{n-x}\\\\=\frac{n!}{x!(n-x)!} p^{x} (1-p) ^{n-x}\\=\frac{6!}{2!4!}(.05)^{2}(.95)^{4}\\= 0.03\\$

probability that exactly two have the metabolic defect is 0.03

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3 years ago

What is the approximate radius of the disc if the area is 78.5 square inches?

Shtirlitz [24]

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