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marta [7]
3 years ago
9

Consider a population of size N = 100 with the three individual mutants with relative growth rate rA = 2, rB = 1.01, and rC = 0.

99. What is the probability that each of the three mutants will take over the population?
Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
7 0

Answer 1 / 25

Step-by-step explanation:

The probability that the first

of the three mutants will take over the population = 2 / 100

The probability that the second

of the three mutants will take over the population = 1.01 / 100

The probability that the third

of the three mutants will take over the population = 0.99 / 100

Therefore, the probability that each of the three mutants will take over the population = probability of the first,second or third = 2 / 100 + 1.01 / 100 + 0.99 / 100 = (2+1.01+0.99)/100 = 4 / 100 = 2/25

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P (-2,6), Q (9,6), R (7, -1), S (-4, -1) are the vertices of a quadrilateral.
vova2212 [387]

Step-by-step explanation:

Parallelogram

Reflect y=-1 ;x changes sign

6 0
3 years ago
36 workers I need 1 pen for each worker. For every 3 people who prefer red pens,there are 9 who prefer blue. How many blue pens
Klio2033 [76]
Blue 9 x 3 = 27
red 3 x 3 = 9
27 + 9 = 36
I hope this helps
7 0
3 years ago
Read 2 more answers
Prove the following using a direct proof:
hodyreva [135]

Answer:

Step-by-step explanation:

Prove: That the sum of the squares of 4 consecutive integers is an even integer.

An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.

Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;

5^{2} = 25

6^{2} = 36

7^{2} = 49

8^{2} = 64

The sum of the squares = 25 + 36 + 49 + 64

                                       = 174

Also,

Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;

-10^{2} = 100

-11^{2} = 121

-12^{2} = 144

-13^{2} = 169

The sum of the squares = 100 + 121 + 144 + 169

                                     = 534

Therefore, the sum of the squares of 4 consecutive integers is an even integer.

8 0
3 years ago
Please answer ASAP!!!
drek231 [11]
Hi there!
------------------------
question - A 36-foot flagpole casts a 10 3/4 foot shadow, while the hospital nearby casts a 37 5/8 foot shadow. Find the height of the hospital
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if you correctly work this out the answer is:
The height of the hospital is 35 3/4 feet
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Have a nice day!
6 0
3 years ago
Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter
hoa [83]

Answer:

0.20 and 0.36

Step-by-step explanation:

y(t) = 2 sin (4π t) + 5 cos (4π t)

We wish to convert this to:

y = A sin(ωt + φ)

We know that ω = 4π.  We also know the following:

5 = A sin φ

2 = A cos φ

Divide the first equation by the second equation:

5/2 = tan φ

φ = tan⁻¹(5/2)

Now, square the two equations and add them together.

5² + 2² = (A sin φ)² + (A cos φ)²

29 = A²

A = √29

The equation of the wave is therefore:

y = √29 sin(4π t + tan⁻¹(5/2))

The maximum negative position is -√29.  And half of that is -½√29.

-½√29 = √29 sin(4π t + tan⁻¹(5/2))

-½ = sin(4π t + tan⁻¹(5/2))

7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)

7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π

t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24

Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.

t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24

t ≈ 0.20 or 0.36

5 0
2 years ago
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