Mathematics, 29.01.2020 03:48 bluenblonderw

South america butterfly at butterfly park is 5: 3 and europe butterflies are 3: 2 and 30 north america at butterfly park. how many south america butterfly are there and how many european butterfly are there

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Answer from: minileiva211

There are 18 South American butterflies and 12 European butterflies.

Step-by-step explanation:

The question is incomplete so the complete question is below:

The ratio of North American butterflies to South American butterflies at a butterfly park is 5:3.The ratio of South American butterflies to European butterflies is 3:2. There are 30 North American butterflies at the butterfly park.

How many South American butterflies are there and how many European butterflies are there ?

Now, to find the number of South American butterflies European butterflies are there.

Let the number of South American butterflies be

The North American butterflies = 30.

As, given the ratio of North American butterflies to South American butterflies at a butterfly park is 5:3.

So, 5 is equivalent to 3.

Thus, 30 is equivalent to

Now, to get the number of South American butterflies by using cross multiplication method:

$\frac{5}{3} =\frac{30}{x}$

By cross multiplying we get:

5x=90

Dividing both sides by 5 we get:

x=18.

The number of South American butterflies = 18.

Now, to get the number of European butterflies:

Let the number of European butterflies be

As, given the ratio of South American butterflies to European butterflies is 3:2.

So, 3 is equivalent to 2.

Thus, 18 is equivalent to .

So, to solve by using cross multiplication method:

$\frac{3}{2} =\frac{18}{y}$

By cross multiplying we get:

3y=36

Dividing both sides by 3 we get:

y=12.

The number of European butterflies = 12.

Therefore, there are 18 South American butterflies and 12 European butterflies.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

step-by-step explanation:

because that's the answer

The stem-and-leaf plot above lists the number of ingredients found in different industrial cleaners.

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