Hi!
46 out of 200 are short haired, which means that 200 - 46 = 154 out of 200 are not short haired. In percentages, that is:
154/200 = 77/100 = 77%
Hope this helps!
The answer can either be two to the 7th power or 128
The region in question is the set
or equivalently,
Cross sections are taken perpendicular to the y-axis, which means each section has a base length equal to the horizontal distance between the curve y = x³ and the line x = 0 (the y-axis). This horizontal distance is given by
y = x³ ⇒ x = ∛y
so that each triangular cross section has side length ∛y.
The area of an equilateral triangle with side length s is √3/4 s², so each cross section contributes an infinitesimal area of √3/4 ∛(y²).
Then the volume of this solid is
I've attached some sketches of the solid with 16 and 64 such cross sections to give an idea of what this solid looks like.
First, find the LCD of the two fractions.
Multiples of 12: 12, 24, 36, 48, 60.
Multiples of 20: 20, 40, 60
The LCD is 60.
Second, change the denominators to be the same as the LCD.
Third, 5 × 5 = 25 / 12 × 5 = 60 / 3 × 3 = 9 / 20 × 3 = 60
Fourth, combine the denominators.
Fifth, subtract 25 - 9 to get 16.
Sixth, find the GCF of 16 and 60.
The GCF is 4.
Seventh, divide the numerator by the GCF.
÷
Eighth, divide the denominator by the GCF.
÷
Ninth, rewrite the fraction in simplest form.
Answer as fraction:
Answer as decimal: 0.2667