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balu736 [363]
2 years ago
15

A population of 200 animals is decreasing by 4% per year. At this rate, in how many years will the population be less than 170?

Mathematics
2 answers:
djyliett [7]2 years ago
8 0
The population will be less that 170 in 4 years
polet [3.4K]2 years ago
5 0

In the question , it is given that the population is decreasing by 4% per year .

So we have to use the following formula of exponential decay:

P(t) = P_{0} (1-r)^t

Substituting the given values, we will get

170 = 200(1-0.04)^t

Dividing both sides by 200

\frac{170}{200} = (0.96)^t

Taking log on both sides

log (\frac{170}{200}) =log (0.96)^t

log (\frac{170}{200}) =t*log (0.96)

Dividing both sides by log(0.96)

\frac{ log (\frac{170}{200}) }{log(0.96) } =t

t = approx 4 years

So after 4 years , the population will be less than 170.


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$28.

Step-by-step explanation:

p(x) = -2(x - 9)^2 + 100

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p(15) = -2(15 - 9)^2 + 100

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5 0
2 years ago
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Solve the triangle. A = 46° a = 33 b = 26
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Using sin rule:
a/sin A =b/sin B=c/sin c
SIN A=sin 46=0.72
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A certain temperature measurement is performed 500 times. The mean value is 0 deg F and the standard deviation is 1 deg F. Assum
egoroff_w [7]

Answer:

477

Step-by-step explanation:

Given that:

Number of trials (n) = 500

Mean (m) = 0

Standard deviation (s) = 1

how many readings fall within +/- 2.000 deg F of the mean value

Mean of 0 and standard deviation of 1

P(-2 ≤ x ≤ 2)

Using the Z probability calculator :

P(x ≤ 2) = 0.97725 ;

P(x ≤ - 2) = 0.02275

Hence :

P(x ≤ 2) - P(x ≤ - 2) = 0.97725 - 0.02275 = 0.9545

Hence, number of readings in 500 trials:

0.9545 * 500 = 477.25

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6 0
1 year ago
2. A boy and his father played 26 games of checkers. For every game the boy lost, he gave his father 5 cents. For every game the
trasher [3.6K]

Answer: the boy won 10 games

Step-by-step explanation:

Let's call B as the number of games won by the boy, and F as the number of games won by the father.

We know that, there is a total of 26 games:

B + F = 26.

We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:

B*8 + F*(-5) = 0.

Then we have a system of equations:

B + F = 26

8*B - 5*F = 0.

The first step is isolating one of the variables. Let's start isolating F in the first equation:

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F = 26 - B.

Now we can replace this in the second equation:

8*B - 5*F = 0

8*B - 5*(26 - B) = 0

8*B + 5*B - 5*26 = 0

13*B = 5*26

B = 5*26/13 = 5*2 = 10

So the boy won 10 games (then the father won the other 16 games)

7 0
2 years ago
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