The brown jug has paid annual dividends of $0.61, $0.64, $0.71, $0.82, and $0.88 per share over the past 5 years, respectively. what is the geometric average dividend growth rate for this period?

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a. 8.51 percent
b. 8.97 percent
c. 9.10 percent
d. 9.59 percent
e. 10.21 percent

Option (d) 9.59%

Explanation:

Data provided in the question:

Annual dividends paid by the Brown jug

$0.61, $0.64, $0.71, $0.82, and $0.88 per share over the past 5 years

Now,

Present value = $0.61

Future value = $0.88

Time = 4 years                    [as there is no interest for the year 1]

Now,

Future value = Present value × (1 + r )ⁿ

here,

r is the geometric average dividend growth rate

$0.88 = $0.61 × (1 + r )⁴

or

(1 + r )⁵ = 1.4426

or

1 + r = 1.0959

or

r = 0.0959

or

r = 0.0959 × 100% = 9.59%

Hence,

Option (d) 9.59%

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

according to the song of roland, the characteristics of an ideal knight are: loyalty to the king, skilled warriors and horseman, valiant, bold, courageous, strong and proud in battle. they should be determined to fulfil their duties and willing to die to make their people safe.