Question

Referring to Exercise 43, the annual report of Dennis
stockholder equity for the same 5-year period (in percent): 13.2, 5.0, 10.2, 17.5, and 12.9.
a. What is the arithmetic mean return?
b. What is the variance?
Plywood Inc. reported these returns on stockholder equity for the past 5 years: 4.3. 4.9.
7.2. 6.7, and 11.6. Consider these as population values.
a. Compute the range, the arithmetic mean, the variance, and the standard deviation.
b. Compare the return on stockhoider equity for Plywood Inc. with that for Dennis Indus-
tries cited in Exercise 44.
The annual incomes of the five vice presidents of TMV Industries are $125,000; $128,000:
$122.000; $133.000: and $140,000. Consider this a population.
a. What is the range?
b. What is the arithmetic mean income?
c. What is the population variance? The standard deviation?
d. The annual incomes of officers of another firm similar to TMV Industries were also stud-
ied. The mean was $129,000 and the standard deviation $8.612. Compare the means
and dispersions in the two firms.
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Answer 1

Answer:

$\orange{ \mathbb{ \large{ \huge{Hello}}}}$

${\huge{\sf{\blue{\underline {\underline{Question}}}}}}$

Find the area of a triangle, two sides of which are 18cm and 10cm and the perimeter is 42 cm :

Answer :-

Given that,

Two sides of triangle are 18 cm and 10 cm.

Perimeter of triangle is 42 cm

Let, third side of triangle be x .

So,

⟶ Perimeter = 18 + 10 + x

⟶ 42 = 28 + x

⟶ 42 - 28 = x

⟶ x = 14

Third side of triangle is 14 cm.

Now,

s = 42/2

s = 21

Semi-perimeter is 21 cm.

Area of traingle :

⟶ √21 × (21 -18)(21 -14)(21 - 10)

⟶ √21 × 3 × 7 × 11

⟶ √3 × 7 × 3 × 7 × 11

⟶ 3 × 7 √11

⟶ 21 × √11

Put √11 = 3.316

⟶ 21 ×3.316

$\longrightarrow \blue{\boxed{\bold{69.639}}\bigstar}$

★

Area of triangle is 69.636 cm²

_____________________________________

Formulas used:-

• Perimeter of triangle = Sum of all sides

• Heron's formula that is

Area of traingle = √s(s - a)(s - b)(s - c)

where,

s is semi-perimeter of triangle.

a, b and c are sides of triangle.

• Semi-perimeter = Perimeter of triangle/2