Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)2 (5 points)

Mathematics

1 answer:

leva [86]2 years ago

4 0

Answer:

g(x) is always decreasing

Step-by-step explanation:

Step 1: Distribute

g(x) = 4 - (2x - 12)

g(x) = 4 - 2x + 12

Step 2: Combine like terms

g(x) = -2x + 16

Since the line is linear and has a negative slope, it will always decrease when you input either a positive or negative x value. The output y will go lower.

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This is the 4th question

gavmur [86]

Answer:

a) There are 9 outcomes.

b) **i have attached the tree diagram**

c) 1/9

d) 1/9

Step-by-step explanation:

Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.

a) For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m • n ways. So for this problem, you would do 3 • 3 which equals 9.

b) **tree diagram is attached**

c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)

The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.

1/3 * 1/3 = 1/9

d) You would do the same thing here as part c.

The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.

1/3 * 1/3 = 1/9

I hope this was helpful!! :)