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2 years ago

Una población de bacterias crece de tal manera que la razón de crecimiento en el instante t (medido en horas) es igual a

Mathematics

1 answer:

Kazeer [188]2 years ago

6 0

By the fundamental theorem of calculus, if

p'(t) = 90t + 500/(1 + t)

and p(0) = 2000, then

p(t) = p(0) + ∫₀ᵗ p'(u) du

⇒ p(t) = 2000 + ∫₀ᵗ (90u + 500/(1 + u)) du

⇒ p(t) = 2000 + (45u² + 500 ln|1 + u|)₀ᵗ

⇒ p(t) = 2000 + 45t² + 500 ln|1 + t|

Then after t = 3 hours, the population of bacteria would be

p(3) = 2000 + 45•3² + 500 ln(1 + 3) ≈ 3098

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g A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of pa

adoni [48]

Complete Question

A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?

Answer:

The value required is $\sigma = 0.0133$

Step-by-step explanation:

From the question we are told that

The upper specification is $USL = 1.68 \ mm$

The lower specification is $LSL = 1.52 \ mm$

The sample mean is $\mu = 1.6 \ mm$

The standard deviation is $\sigma = 0.03 \ mm$

Generally the capability index in mathematically represented as

$Cpk = min[ \frac{USL - \mu }{ 3 * \sigma } , \frac{\mu - LSL }{ 3 * \sigma } ]$

Now what min means is that the value of CPk is the minimum between the value is the bracket

substituting value given in the question

$Cpk = min[ \frac{1.68 - 1.6 }{ 3 * 0.03 } , \frac{1.60 - 1.52 }{ 3 * 0.03} ]$

=> $Cpk = min[ 0.88 , 0.88 ]$

$Cpk = 0.88$

Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2

Now let assuming that

$\frac{\mu - LSL }{ 3 * \sigma } = 2$

$\frac{ 1.60 - 1.52 }{ 3 * \sigma } = 2$

=> $0.08 = 6 \sigma$

=> $\sigma = 0.0133$

$\frac{ 1.68 - 1.60 }{ 3 * 0.0133 }$

=> $2$

Hence

$Cpk = min[ 2, 2 ]$

$Cpk = 2$

So $\sigma = 0.0133$ is the value of standard deviation required

3 0

3 years ago

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

oksian1 [2.3K]

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

45% chance that the land has oil.

This means that $P(A) = 0.45$

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that $P(B|A) = 0.8$

What is the probability that the land has oil and the test predicts it?

This is $P(A \cap B)$ . So

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36$

0.36 = 36% probability that the land has oil and the test predicts it

5 0

2 years ago

Find the value of x in the triangle shown below.

kobusy [5.1K]

Answer:

u did a lot of this budy a lot of these

Step-by-step explanation:

8 0

2 years ago

You and six friends play a game or each person writes down his or her name on a scrap of paper and then the names are randomly d

Nostrana [21]

1 on 7 is the answer!

4 0

3 years ago

Read 2 more answers

Atriangle was translated 4 units down.

loris [4]

Answer:

Idk if this is right but I think it's The transformed shaped shifted 7 units to the right so add 7 to x and it shifted 6 units down so subtract 6 from y.

The answer is (x,y) = (x+7) (y-6)

Hope this helps!!!?

7 0

3 years ago

Read 2 more answers