In a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. there are 450 total flying insects.

(a) create a table for how many butterflies there are for 1, 50, and 100 flying insects. show your work.

(b) how many butterflies are in the conservatory? show your work.

a)

number of flying insects                       number of butterflies

           1                                                                 9/25

           50                                                               18

          100                                                             36

b)

162 butterflies

Step-by-step explanation:

Let 'x' denotes the variable such that 36x denotes the number of butterflies and 100x denotes the number of flying insects and the ratio of butterflies to total number of flying insects is 36 to 100 (i.e. ).

As there are total 450 flying insects.

This means that 100x=450

⇒  x=4.5 ( since on dividing both side of the equality by 100).

Hence the number of butterflies are 36x=162.----(1).

(a)

Since for 1 flying insect 100x=1

⇒  x=1/100

Hence 36 x=36×(1/100)=36/100=9/25

for 50 flying insects.

100x=50

⇒ x=1/2

Hence, 36x=36×(1/2)=18

Similarly is the way to compute for 100 flying insects.

   number of flying insects                       number of butterflies

           1                                                                 9/25

           50                                                               18

          100                                                             36

(b)

In the conservatory there are 162 butterflies.( as computed above in equation (1))

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.