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3 years ago

Find the area of the following polygons: Given: AC = 12, AD = 16

Mathematics

2 answers:

Kisachek [45]3 years ago

6 0

38 is the correct answer

IrinaVladis [17]3 years ago

4 0

38 is the answer I think

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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

7 0

3 years ago

The quotient of a number n and 12 is written how?<br><br> A. 12/n<br><br> B. n/12

Whitepunk [10]

The quotient of <em>n</em> and 12.

Note that n is first, then 12.

B. n/12 is your answer

hope this helps

5 0

4 years ago

Read 2 more answers

how do i Write “345 ants per 23 square inches” as a unit rate. Round to the hundredths place, if necessary.

butalik [34]

0.07 is the correct answer.

4 0

4 years ago

1. Segment AE is 7 inches and AH is 7^/3 inches. What is the length of EH? Round to the nearest tenth.

Orlov [11]

Answer:

1.) 9.9

2.) 15.6

Step-by-step explanation:

1.) Consider triangle AEH

AEH is a right angle triangle as ∠AEH = 90°

AH is the hypotenuse of the triangle.

Applying Pythagorean theorem

$AE^{2} + EH^{2} = AH^{2}$

substituting values as given in the question:

$7^{2} +EH^{2}=(7\sqrt{3} )^{2}\\EH^{2}=(7\sqrt{3} )^{2}-7^{2} \\EH^{2}=98\\EH=\sqrt{98}\\EH=7\sqrt{2}$

∴ EH≈9.9

2.) Consider triangle CDF

CDF is a right angle triangle as ∠CDF = 90°

CF is the hypotenuse of the triangle.

Applying Pythagorean theorem

$CD^{2} + DF^{2} = CF^{2}$

substituting values as given in the question:

$11^{2} +DF^{2}=(11\sqrt{3} )^{2}\\DF^{2}=(11\sqrt{3} )^{2}-11^{2} \\DF^{2}=242\\DF=\sqrt{242}\\DF=11\sqrt{2}$

∴ DF≈15.6

3 0

3 years ago

Read 2 more answers

I'm stuck on this. Please help!!

Sveta_85 [38]

I think it is F, but I am a not sure.

3 0

4 years ago

Read 2 more answers