a. A proper joint density function is established if, within its support, it remains non-negative and its integral totals 1. The first requirement is satisfied provided that
. Meeting the second stipulation necessitates integrating over
. b. To derive the marginal joint density of
and
, integrate the joint density concerning
. Next, you can obtain the desired probability by integrating the joint density.
Answer: To remove fractions prior to solving, each term in the equation must be multiplied by 
.
Step-by-step explanation:
Consider the given expression:
It is essential to simplify this before attempting to solve it.
Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.
Break down the denominators into their prime components:
Select 
, as it possesses the greatest exponent. Thus:
Ultimately, to remove the fractions before solving, multiply both sides by 4:
Answer:
m = - 3
Step-by-step explanation:
a³ + 27 can be recognized as a sum of cubes, which factors generally as
a³ + b³ = (a + b)(a² - ab + b²). Therefore:
a³ + 27
= a³ + 3³
= (a + 3)(a² - 3a + 9).
By comparing a² - 3a + 9 to a² + ma + 9, we find that
m = - 3.
