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2 years ago

15

Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population for the fish of that species

in that lake) to be 6,000. The number of fish tripled in the first year.
(a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.

P =

(b) How long will it take for the population to increase to 3000? (Round your answer to two decimal places.)

=yr

1 answer:

LUCKY_DIMON [66]2 years ago

6 0

Answer:

2.30 years

Step-by-step explanation:

The number of fish tripled in the first year, making a total of 240 * 3 = 720 fishes.

(a) The formula for logistic equation is as the following

$P = P_0e^{kt}$

where P0 = 240 is the number of fishes initially, we can plug in P = 720 and t = 1 to calculate the constant k

$720 = 240e^{1k}$

$e^k = 3$

$k = ln3 = 1.1$

b) Using the following formula

$P = P_0e^{kt}$

with P = 3000, P0 = 240, k = 1.1, we can calculate the number of years it takes to get to 3000 fishes

$3000 = 240e^{1.1t}$

$12.5 = e^{1.1t}$

$1.1t = ln12.5 = 2.53$

$t = 2.30 years$

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vodka [1.7K]

Answer:

a. 0.71

b. 0.9863

Step-by-step explanation:

a. From the histogram, the relative frequency of houses with a value less than 500,000 is 0.34 and 0.37

-#The probability can therefore be calculated as:

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Hence, the probability of the house value being less than 500,000 is o.71

b.

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$P(\bar X$

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2 years ago

Lian invested an amount of money at an interest rate of 5.2% per year.

Zigmanuir [339]

Answer:

$6500

Step-by-step explanation:

Let the amount of money invested by Lian be $x

Interest rate = 5.2% per year

interest earned in first year will be 5.2% of amount of money invested by Lian .

(note: since in first year there will be no interest accrued on interest so interest for first year is simple interest )

interest earned in one year if money invested by Lian is $x

= 5.2% of $x (1)

But , it is given in one year she received interest of 338 dollars

so, 338 dollars must be equal to 5.2% of $x

equating $338 with 5.2% of $x , we have

5.2% of x = 338

=> (5.2/100) * x = 338

=>5.2 x = 338*100

=> x = 33800/5.2 = 6500.

Thus, amount of money Lian invested is $6500.

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1 year ago

In college basketball, some teams get most of their points from just one player, and other teams are more balanced in scoring. C

lutik1710 [3]

Answer:

(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.

(D)The mean number of points per player per game is the same at all 3 schools.

Step-by-step explanation:

<u>Baylor University</u>

6 players who each score 12 points per game

6 players who each score 0 points per game.

The Scores are: 0,0,0,0,0,0,12,12,12,12,12,12

$Mean=\frac{0+0+0+0+0+0+12+12+12+12+12+12}{12} \\Mean=6\\Median=\frac{12+0}{2}=6$

<u>University of Maryland</u>

1 player scores 58 points per game,

1 player scores 14 points per game,

The rest(10) of the players score 0 points per game.

The Scores are: 0,0,0,0,0,0,0,0,0,0,14,58

$Mean=\frac{0+0+0+0+0+0+0+0+0+0+14+58}{12} \\Mean=6\\Median=\frac{0+0}{2}=0$

<u> Dartmouth College</u>

4 players score 5 points per game,

4 players score 6 points per game,

4 players score 7 points per game.

The Scores are: 5,5,5,5,6,6,6,6,7,7,7,7

$Mean=\frac{5+5+5+5+6+6+6+6+7+7+7+7}{12} \\Mean=6\\Median=\frac{6+6}{2}=6$

The following applies:

(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.

(D)The mean number of points per player per game is the same at all 3 schools.

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1 year ago

NEED HELP ASAP!!!!!

katen-ka-za [31]

If restaurant rotates $60^{0}$ every 15 minutes, then after one hour it will rotate $60^{0}*4=240^{0}$ .
When restaurant makes full rotation $360^{0}$ , the length will be $2 \pi r=2 \pi *80=160\pi$ . But $240^{0}$ <span>is only $\frac{2}{3}$ from the full rotation, so the bird will pass $160\pi * \frac{2}{3} =335$ ft
</span><span>
</span><span>Answer: B is a correct choice
</span>

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2 years ago

Which is a solution to the equation? (x −2)(x + 5) = 18 x = −10 x = −7 x = −4 x = −2

Leona [35]

Answer:

Solutions:

$x=-7$

$x=4$

Step-by-step explanation:

$(x-2)(x + 5) = 18$

Expanding the factored form:

$x^2+5x-2x-10=18$

$x^2+3x-28=0$

Factoring the second-degree polynomial:

$(x+7)(x-4)=0$

This is true for

$x=-7 \text{ or } x=4$

4 0

1 year ago