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natulia [17]
3 years ago
5

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate

parameter of 7.6% per hour. How many hours does it take for the size of the sample to double?
Mathematics
1 answer:
Kazeer [188]3 years ago
7 0
Set the growth factor equal to 2
e^{.076 t} = 2
Solve for t, Take natural log of both sides
ln (e^{.076 t}) = ln(2)  \\  .076 t = ln(2)  \\ ........ \\  t = \frac{ln (2)}{.076}
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) Determine the probability that a bit string of length 10 contains exactly 4 or 5 ones.
yanalaym [24]

Answer: 0.4512

Step-by-step explanation:

A bit string is sequence of bits (it only contains 0 and 1).

We assume that the  0 and 1 area equally likely to any place.

i.e. P(0)= P(1)= \dfrac{1}{2}

The length of bits : n = 10

Let X = Number of getting ones.

Then , X \sim Bin(n=10,\ p=\dfrac{1}{2})

Binomial distribution formula : P(X=x)=^nC_x p^x q^{n-x} , where p= probability of getting success in each event and q= probability of getting failure in each event.

Here , p=q=\dfrac{1}{2}

Then ,The probability that a bit string of length 10 contains exactly 4 or 5 ones.

P(X= 4\ or\ 5)=P(x=4)+P(x=5)\\\\=^{10}C_4(\dfrac{1}{2})^{10}+^{10}C_4(\dfrac{1}{2})^{10}

=\dfrac{10!}{4!6!}(\dfrac{1}{2})^{10}+\dfrac{10!}{5!5!}(\dfrac{1}{2})^{10}

=(\dfrac{1}{2})^{10}(\dfrac{10!}{4!6!}+\dfrac{10!}{5!5!})

=(\dfrac{1}{2})^{10}(210+252)

=(0.0009765625)(462)

=0.451171875\approx0.4512

Hence, the  probability that a bit string of length 10 contains exactly 4 or 5 ones is 0.4512.

3 0
4 years ago
Between which two integers does 35 lie?
iren2701 [21]

The answer is the first choice, "5 and 6."

The square root of 35 is equal to 5.92, which is in between the numbers 5 and 6.

7 0
3 years ago
A scientist plans to study exotic birds in the rain forest. The helicopter
AlladinOne [14]

Answer:

2 days

Step-by-step explanation:

For the flight to and from it will cost a total of $998

We subtract the flight from the budget, which leaves us with $285

Next, we subtract 1 day from $285 which is $112

That leaves us with $173.

We then subtract one mire day ($112) which leaves us with $61

8 0
2 years ago
what is the probability of A is 0.8, what is the probability of B is 0.45, what is the probability of either A and B is 0.30?​
Degger [83]

Answer:

<h3>you need to be more clear</h3>

Step-by-step explanation:

i am confused

8 0
2 years ago
How do u add and subtract negative fractions?
Montano1993 [528]
It’s just like solving a positive fraction find a common denominator and Add or subtract
4 0
3 years ago
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