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Zielflug [23.3K]

2 years ago

9

The population P(t) of a bacteria culture is given by P(t)=−1,500t2+48,000t+18,000, where t is the time in hours after the cultu

re is started. Determine the time(s) at which the population will be greater than 388,500 organisms.

1 answer:

Anna [14]2 years ago

6 0

Answer:

this is a tough question

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n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

4 0

2 years ago

The meat department of a supermarket sells ground beef in approximate 1 lb packages, but there is some variability. A random sam

grin007 [14]

Answer:

1.05 ± 0.05 lbs

Step-by-step explanation:

Hi!

We can calculate this interval with the z-score of the 90% which is (by convention) 1.645

The interval is calculated as follows:

$x_m \pm 1.654(\frac{\sigma}{\sqrt n})$

where x_m is the mean, σ the standar deviation and n is the number of samples:

replacing these values we get:

$1.05 \pm (1.645 \times \frac{0.23}{\sqrt 65})\\1.05 \pm 0.046$

*rounded to the first decimal*

1.05 ± 0.05

6 0

2 years ago

A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb

Kobotan [32]

Answer:

2,500 German chocolate cake boxes.

1,500 Swiss chocolate cake boxes.

Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

$0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700$

Solving the linear system above:

$(0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500$

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

6 0

2 years ago

The value of which of these expressions is closest to e ?

snow_tiger [21]

Answer:

It's A, Apex confirmed

Step-by-step explanation:

3 0

2 years ago

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Eight students are competing for a blue, red, and yellow ribbon for their agriculture project. How many different ways are there

Andreyy89

Answer:

the answer is B.336

Step-by-step explanation:

got it right on ed

4 0

2 years ago

Read 2 more answers