If 42 butterflies were seen in 3 hours at that rate how many butterflies were seen per hour

14 butterflies per hour

Step-by-step explanation: "Per hour" means in 1 hour so we can rewrite the given statement using fractions.

42 butterflies over 3 hours = ___ butterflies per hour.

I have attached my work in the image provided.

To find out what goes in the blank, notice that we have a 1 in the denominator of our second fraction. So we want to find a fraction that is equivalent to 42/3 that has a 1 in the denominator.

If we divide the numerator and denominator of 42/3 by 3, we get the equivalent fraction 14/1 or 14 butterflies over 1 hour. So now we have 14 butterflies over 1 hour = ___ butterflies per hour.

Now we can easily see that a 14 must go in the blank which means that the unit rate for 42 butterflies in 3 hours is 14 butterflies per hour.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.