PLEASE help
In the last hour, Ellie observed 32 monarchs, 56 gulf fritillaries and 8 giant swallowtails visit her butterfly garden.

If 480 butterflies visit her garden, how many can we expect will be giant swallowtails?

A. 83
B. 160
C. 8
D. 40

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bird10000000 bird10000000 · Answer 1 · 2017-03-14T00:40:31+01:00

she observed 32 monarchs, 56 gulf fritillaries, and 8 swallowtails. First you add those together

32+56+8=?

32+56+8=96

then you set up a proportion. 8 out of every 96 butterflies are swallowtails, so you set this up as a fraction- 8/96

then you must set the two numbers(96 and 480) equal, so you get this proportion. 8/96= X/480

you solve this by cross multiplying. 8 × 480 equals 3840, and then divide 3840 by 96 which equals 40. therefore the answer is...

D) 40

MrRoyal MrRoyal · Answer 2 · 2022-03-17T14:23:55+01:00

We should expect 40 giant swallowtails in 480 butterflies

The given parameters are:

32 monarchs, 56 gulf fritillaries and 8 giant swallowtails

So, the probability that a butterfly is a giant swallowtail is:

[tex]p = \frac{8}{32 + 56 + 8}[/tex]

This gives

[tex]p = \frac{8}{96}[/tex]

Simplify

[tex]p = \frac{1}{12}[/tex]

In 480 butterflies, the expected number of giant swallowtail is:

[tex]E(x) = np[/tex]

So, we have:

[tex]E(x) = 480 * \frac 1{12}[/tex]

Evaluate the product

[tex]E(x) = 40[/tex]

Hence, we should expect 40 giant swallowtails in 480 butterflies