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34kurt
3 years ago
7

The lifetime of a leaf blower is exponentially distributed with a mean of 5 years. If you buy a 12 year old leaf blower, what is

the probability that it will be working after an additional 5 years?
Mathematics
1 answer:
snow_tiger [21]3 years ago
8 0

Answer:

1.967 × 10⁻¹¹

Step-by-step explanation:

This is a conditional probability problem

Probability that a 12 year old leaf blower works for 5 more years = Probabilty that a leaf blower works for 17 years, given that it has worked for 12 years = P(17|12)

P(17|12) = P(17 n 12)/P(12)

P(17 n 12) = P(17)

Exponential random variable is given as

f(x) = λ e^(-λ.x)

λ = rate parameter = 5 years per blower

x = variable whose probability is required = 17

f(17) = 17 e^(-5×17)

f(17) = 17 e⁻⁸⁵ = 2.067 × 10⁻³⁶

f(12) = 12 e^(-5×12)

f(12) = 12 e⁻⁶⁰ = 1.051 × 10⁻²⁵

P(17|12) = (2.067 × 10⁻³⁶)/(1.051 × 10⁻²⁵)

P(17|12) = 1.967 × 10⁻¹¹

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2 years ago
The distance between City A and City B is 250 miles. A length of 2.3 feet represents this distance on a certain wall map. City C
masya89 [10]

The distance between city C and city D is 450 miles.

<u>Solution:</u>

Given, The distance between City A and City B is 250 miles.  

A length of 2.3 feet represents this distance on a certain wall map.  

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We have to find what is the actual distance between City C and City D?

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Answer:

discriminant =0

1 real root

Step-by-step explanation:

The discriminant is b^2 -4ac  

when the equation is written in the form  ax^2 +bx+c

f(x) = 3x^2 +24x+48

a = 3   b = 24 and c =48

discriminant = 24^2 - 4(3)*(48)

                      =576-576

                        =0


If the discriminant >0  we have 2 real roots

if discriminant = 0  we have 1 real root

if discriminant <0 we have 2 complex roots

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