How many roots will the function f(x)= -3x³ - x² + 7x + 6 have?
1 answer:
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Answer:
Ahmed runs 6 miles each day
Step-by-step explanation:
∵ Ahmad runs m miles each day
∵ Ali runs twice as many miles as Ahmad
→ That means Ali runs 2 × m miles each day
∴ Ali runs 2m miles each day
∵ Altogether, they run 18 miles each day
→ Add m and 2m, then equate the sum by 18
∴ m + 2m = 18
∴ 3m = 18
→ Divide both sides by 3 to find m
∵
∴ m = 6
∵ m represents the number of miles that Ahmed runs each day
∴ Ahmed runs 6 miles each day
(1) Looks like the joint density is
In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is
(2) The region in which <em>X</em> > 2 and <em>Y</em> < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is
(3) Are you supposed to find the marginal density of <em>X</em>, or the conditional density of <em>X</em> given <em>Y</em>?
In the first case, you simply integrate the joint density with respect to <em>y</em>:
In the second case, we instead first find the marginal density of <em>Y</em>:
Then use the marginal density to compute the conditional density of <em>X</em> given <em>Y</em>:
