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3 years ago

Help!!!

Mathematics

1 answer:

sesenic [268]3 years ago

6 0

Answer:

Time it will take t = 23.1 (round to the nearest tenth)

Step-by-step explanation:

Given: A population of bacteria is growing exponentially;

According to the model;

$P = 100e^{0.60t}$ ......[1]; where P is the number of colonies and t be the time measured in hours.

After how many hours will 400 colonies be present.

Substitute value of P = 400 in [1];

$400 = 100 e^{0.06t}$

Divide both sides by 100 we get;

$4 = e^{0.06t}$

Taking ln both sides we get;

$ln 4 = ln e^{0.06t}$

Since; $ln e^x = x$

then;

$ln 4 = 0.06 t$

Divide both sides by 0.06 we get;

$t = \frac{ln 4}{0.06}$

$t =\frac{1.38629436112}{0.06} =23.104906$ hours

Therefore, the time it will take is, t = 23.1 (round to the nearest tenth)

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Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

Step-by-step explanation:

We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.

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$\sigma$ = standard deviation of all horses coming to the veterinary clinic = 8 yrs

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Answer:

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Step-by-step explanation:

Data provided

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$\mu$ population mean

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n=601 represent the sample size

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The formula for the confidence interval of the true mean is given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

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