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Masja [62]
3 years ago
9

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours. At this rate of decay,

Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

9,942 bacteria were there at 10 hours.

Step-by-step explanation:

Equation for population decay:

The equation for population decay, after t hours, is given by:

P(t) = P(0)(1-r)^t

In which P(0) is the initial population and r is the decay rate, as a decimal.

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.

This means that P(0) = 200000 and that when t = 18, P(t) = 900. So we use this to find r.

P(t) = P(0)(1-r)^t

900 = 200000(1-r)^{18}

(1-r)^{18} = \frac{900}{200000}

\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}

1 - r = (\frac{900}{200000})^{\frac{1}{18}}

1 - r = 0.7407

So

P(t) = P(0)(1-r)^t

P(t) = 200000(0.7407)^t

At this rate of decay, how many bacteria was there at 10 hours?

This is P(10). So

P(10) = 200000(0.7407)^{10} = 9941.5

Rounding to the nearest whole number:

9,942 bacteria were there at 10 hours.

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to get to work truman waited 11 minutes for the bus, then travled 21.78 miles on the bus at a speed of 33 miles per hour how muc
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4 years ago
A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 1
jekas [21]

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What’s the answer to 21:7
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3?

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4 years ago
Suppose 12% of students are veterans. From a sample of 263 students, how unusual would it be to have less than 22 veterans?
kkurt [141]

Answer:

Yes, both np and n(1-p) are ≥ 10

Mean = 0.12 ; Standard deviation = 0.02004

Yes. There is a less than 5% chance of this happening by random variation. 0.034839

Step-by-step explanation:

Given that :

p = 12% = 0.12 ;

Sample size, n = 263

np = 263 * 0.12 = 31.56

n(1 - p) = 263(1 - 0.12) = 263 * 0.88 = 231.44

According to the central limit theorem, distribution of sample proportion approximately follow normal distribution with mean of p = 0.12 and standard deviation sqrt(p*(1 - p)/n) = sqrt (0.12 *0.88)/n = sqrt(0.0004015) = 0.02004

Z = (x - mean) / standard deviation

x = 22 / 263 = 0.08365

Z = (0.08365 - 0.12) / 0.02004

Z = −1.813872

Z = - 1.814

P(Z < −1.814) = 0.034839 (Z probability calculator)

Yes, it is unusual

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