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Cerrena [4.2K]
3 years ago
8

Please show work if you do, ( and get it right) I will make you brainliest!!!

Mathematics
1 answer:
DerKrebs [107]3 years ago
3 0

Answer:

The percentage increase in bird population in the second years is 4%  .

Step-by-step explanation:

Given as :

During two years, the population of birds of an island became 7 times more than before.

The the percentage increase in first year = = r_1 =40%

Let The percentage increase in second year =  r_2 = r%

So, According to question

The initial population of bird = x

The increase population of bird =7 times before = 7 x

Now,

The increase population of bird = initial population of bird × (1+ \dfrac{r_1}{100}) ×  (1+ \dfrac{r_2}{100})

Or, 7 x = x × (1+ \dfrac{40}{100}) ×  (1+ \dfrac{r}{100})

Or, \dfrac{7 x}{x} = 1.4 ×  (1+ \dfrac{r}{100})

Or, 7 = 1.4 ×  (1+ \dfrac{r}{100})

Or, \dfrac{7 }{1.4} = (1+ \dfrac{r}{100})

Or, 5 = (1+ \dfrac{r}{100})

Or, (1+ \dfrac{r}{100}) = 5

Or, \dfrac{r}{100} = 5 - 1

Or,  \dfrac{r}{100} = 4

∴ r = 4 × 100

I.e r = 400

so, The percentage increase = r% = 4

Hence The percentage increase in bird population in the second years is 4%  . Answer

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How many different perfect cubes are among the positive actors of 2021^2021
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hope this helps :D

Step-by-step explanation:

Perfect cube factors:

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Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

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Perfect square and perfect cube

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3(0 or 6) —– 2 factors

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Let A denotes set of numbers, which are perfect squares.

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2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

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n(A U B )= n(A) + n(B) – n(A∩B)

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