Unit squares are arranged to form a rectangular grid that is m units wide and n units tall, where m and n are positive integers with 2n < m < 3n. The region below one of the diagonals of the rectangle is shaded as shown. For certain pairs m and n, there is a unit square in the grid that is not completely shaded but whose shaded area is greater than 0.999. The smallest possible value of mn for which this is true satisfies (A) 496 ≤ mn ≤ 500 (B) 501 ≤ mn ≤ 505 (C) 506 ≤ mn ≤ 510 (D) 511 ≤ mn ≤ 515 (E) 516 ≤ mn ≤ 520

the probability that a bird is green (.30) is true

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

c

step-by-step explanation:

d .tv

step-by-step explanation:

the side tv is included in both triangles.   this means it corresponds to itself in the transformation.

this is justified by using the reflexive property, which states that anything is congruent to itself.