In the last hour, ellie observed 32 monarchs, 56 gulf fritillaries and 8 giant swallowtails visit her butterfly garden. 0 i if 480 butterflies visit her garden, how many can we expect will be giant swallowtails?

40

Step-by-step explanation:

Developing an initial ratio of the number of giant swallowtails to the total number of observed butterflies, you can then use this ratio to form a proportion (equivalent ratios) to solve for the amount of giant swallowtails expected out of 480:

Since 32 + 56 + 8 = 96, then the original ratio is 8/96.  To find the expected number out of 480:

, where 'x' is the number of giant swallowtails

Cross-multiply: 96x = (8)(480) or 96x = 3840

Divide: 96x/96 = 3840/96

Solve: x = 40

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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