Fatima surveyed a random sample of 80 students in her school about their
favorite type of pet. Of the students surveyed, 20 chose cats as their favorite
type of pet. If there are 597 total students at the school, what would be a valid
estimate for the number of students whose favorite type of pet is a cat?

149

Step-by-step explanation:

out of 80 students, 20 said that they prefers cats, then the relative frequency is:

p =20/80 = 0.25

then, out of the 597 students a estimate of:

N = 0.25*597 = 149.25 like cats

We should round it down so we have a whole number, then we have a estimate of 149 students.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb