3 years ago

What does 6x^2 - 24y^2 equal too

1 answer:

7 0

Simplify the following:
6 x^2 - 24 y^2

Factor 6 out of 6 x^2 - 24 y^2:
6 (x^2 - 4 y^2)

x^2 - 4 y^2 = x^2 - (2 y)^2:
6 (x^2 - (2 y)^2)

Factor the difference of two squares. x^2 - (2 y)^2 = (x - 2 y) (x + 2 y):
Answer: 6 (x - 2 y) (x + 2 y)

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xP(x)00.2510.0520.1530.55Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal pl

Nookie1986 [14]

The Solution:

Given:

Required:

Find the standard deviation of the probability distribution.

Step 1:

Find the expected value of the probability distribution.

$E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)$ $\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}$

Step 2:

Find the standard deviation.

$Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}$ $=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)$ $=4(0.25)+1(0.05)+0(0.15)+1(0.55)$ $=1+0.05+0+0.55=1.60$

Thus, the standard deviation is 1.60

Answer:

1.60