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?
Answer:
40 is the answer
Explanation:
As per the given details, we can expect that 40 of the 480 butterflies that visit Ellie's garden will be giant swallowtails.
What is fraction?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator.
Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.
The total number of butterflies observed in the last hour is:
32 + 56 + 8 = 96
This represents the fraction of the total butterflies that were observed, and we can set up a proportion to solve for the number of giant swallowtails in the total population:
8/96 = x/480
Multiplying both sides by 480, we get:
x = (8/96) * 480
x = 40
Therefore, we can expect that 40 of the 480 butterflies that visit Ellie's garden will be giant swallowtails.
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The triangles below are similar. The ratio of the lengths of corresponding sides is 49 . a. What is the ratio (smaller to larger) of the perimeters? b. What is the ratio (smaller to larger) of the areas? The image is of two similar triangles with proportionate side of each marked as 4 in. and 9 in. respectively.
Answer:
a.) 4 : 9
b.) 16 : 81
Explanation:
a.) Ratio of perimeter will still be
4 : 9
b.) The two similar triangles ΔABC and ΔDEF as shown from the attached figures. That is
AB/DE = AC/DF = BC/EF
It is apparent that ΔAPB and ΔDEQ are also similar as all respective angles are equal. Hence,
AB/DE = AP/DQ = BP/EQ
Moreso ΔABC = 1/2 × BC × AP and ΔDEF = 1/2 × EF × DQ and
ΔAPB/ΔDEQ = BC/EF × AP/DQ
But
AP/DQ = AB/DE = BC/EF
and hence
ΔAPB/ΔDEQ = BC/EF × BC/EF
= BC^2/EF^2 and as
BC/EF = AC/DF = AB/DE
ΔAPB/ΔDEQ = AC^2/DF^2 = BC^2/EF^2
= AB^2/DE^2
Hence if sides of two similar triangles are in the ratio a:b, their areas are in the proportion a^2:b^2
As in given case sides are in the ratio of 4:9.
ratio of their areas is 4^2:9^2 or 16:81.
The ratio (smaller to larger) of the perimeters of this similar triangle is equal to 4:9 and 16:81 for their areas.
Given the following data:
Ratio = 4:9Side length of smaller triangle = 4 inches.Side length of larger triangle = 9 inches.What is a triangle?A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
How to calculate the perimeter of a triangle.Mathematically, the perimeter of a triangle is given by this formula:
[tex]P=A+B+C[/tex]
Where:
A, B, and C are length of sides.What is scale factor?Scale factor can be defined as the ratio of two (2) corresponding length of sides in two similar geometric figures such as equilateral triangles.
In Geometry, if the scale factor of two (2) similar geometric figures is given as a:b, then;
The ratio of their perimeters is equal to a:b.The ratio of their areas is equal to [tex]a^2:b^2[/tex].In conclusion, the ratio (smaller to larger) of the perimeters of this similar triangle is equal to 4:9. Also, the ratio (smaller to larger) of their areas is equal to [tex]4^2 :9^2=[/tex] 16:81.
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