6x^2-2.4=0 show all answers I need the answer desperatly

let x = the amoun of raw sugar in tons a procesing plant is a sugar refinery process in one day . suppose x can be model as expo

anygoal [31]

Answer:

The answer is below

Step-by-step explanation:

A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?

Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:

$f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\$

a) P(x > 5) = $\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865$

b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.

That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757

c) Let b be the amount of raw sugar should be stocked for the plant each day.

P(x > a) = $\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}$

But P(x > a) = 0.05

Therefore:

$e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98$

a ≅ 12

6 0

2 years ago

Which expression is equivalent to 4 sqrt 24x^6y/128x^4y^5

Stels [109]

The first step for finding out if the expression provided is equivalent to $\sqrt{4}$ is to reduce the fraction with $x^{4}$ .
$\frac{24 x^{2} y}{128 y^{5} }$
Now reduce the fraction with y.
$\frac{24 x^{2} }{128 y^{4} }$
Finally,, reduce the fraction with 8 to get your final answer.
$\frac{3 x^{2} }{16 y^{4} }$
Let me know if you have any further questions.
:)

5 0

2 years ago

There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been

slamgirl [31]

There are 400 balcony seats in the concert hall.

Step-by-step explanation:

Step 1 :

The number of lower seats = 450 seats

Total seats = Lower seats + balcony seats

Step 2 :

Tickets sold = 170 tickets
Total tickets = x

Tickets sold = 1/5 of total tickets.

⇒ 170 = (1/5)x

⇒ x = 5 $\times$ 170

⇒ x = 850 tickets

∴ Total seats in the concert hall is 850.

Step 3 :

Total seats = 450 + balcony seats

850 - 450 = balcony seats

∴ balcony seats = 400

7 0

2 years ago

A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by dP dt = kP − h

Vadim26 [7]

It increases at T because the behavior increased its speed

8 0

2 years ago

In Rhode Island, sales tax is 7.0%. What is the tax on items that total $140.88 before tax?

Paraphin [41]

9.86 is the sales tax

6 0

2 years ago

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