4. The roots of the equation x2 + 16 = 4bx are real if :

Mathematics

1 answer:

dezoksy [38]4 years ago

6 0

Answer:

b < - 2 or b > 2

Step-by-step explanation:

Given

x² + 16 = 4bx ( subtract 4bx from both sides )

x² - 4bx + 16 = 0 ← in standard form

with a = 1, b = - 4b, c = 16

For the roots to be real the discriminant b² - 4ac > 0, that is

(- 4b)² - (4 × 1 × 16) > 0

16b² - 64 > 0

16(b² - 4) > 0 ← factor using difference of squares

16(b - 2)(b + 2) > 0, thus

b < - 2 or b > 2

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Internet Pricing An Internet Service Provider (ISP) offers its customers three options:

Mama L [17]

Answer:

(b)$29.62

(c)$5.73

Step-by-step explanation:

Basic: Standard internet for everyday needs, at $24.95 per month.

Premium: Fast internet speeds for streaming video and downloading music, at $30.95 per month.

Ultra: Super-fast internet speeds for online gaming at $40.95 per month.

Let the number of customers on Ultra=x; therefore:

Number of Premium customers =2x

Number of Basic customers =3x

Total=x+2x+3x=6x

$P(Ultra)=\dfrac{x}{6x}=\dfrac{1}{6} \\P(Premium)=\dfrac{2x}{6x}=\dfrac{1}{3}\\P(Basic)=\dfrac{3x}{6x}=\dfrac{1}{2}$

(a)X=Monthly fee paid by a randomly selected customer.

Therefore, the probability distribution of X is given as:

$\left|\begin{array}{c|c}X&P(X)\\---&---\\\$24.95&3/6\\\$30.95&2/6\\\$40.95&1/6\end{array}\right|$

(b)Average Monthly Revenue per customer

Mean,

$\mu=(\$24.95 \times 3/6)+(\$30.95 \times 2/6)+(\$40.95 \times 1/6)\\=\$29.62$

(c)Standard Deviation

$\left|\begin{array}{c|c|c|c|c}x&P(x)&x-\mu &(x-\mu)^2&(x-\mu)^2P(x)\\-----&-----&----&----&-----\\\$24.95&3/6&-4.67&21.8089&10.9045\\\$30.95&2/6&1.33&1.7689&0.5896\\\$40.95&1/6&11.33&128.3689&21.3948\\-----&-----&----&----&-----\\&&&&32.8889\end{array}\right|$