Solution
To determine the vertical translation
We need to determine the amplitude
The amplitude is

Since the minimum is 4
Hence, the Vertical shift is 3+4 = 7
Part B
Given f(x) = 4 sin(θ - 45) + 8
The vertical translation is 8
We define the probability of a particular event occurring as:

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are <em>independent</em>, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for <em>each </em>of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.
Now that we've found the number of possible outcomes, we need to find the number of <em>desired</em> outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is <em>at least one 5 rolled</em>. It turns out, there are only 3:
(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5
So, we have

probability of rolling at least one 5.
According to Adam Smith, self interest and competition act as an invisible hand, guiding firms in a market-based economy.
Answer:
1.35kg
Step-by-step explanation:
450g : 6 people
x : 18 people
To get from 6 to 18, multiply by 3 so do the same to the other side
450 × 3 = 1350g
To convert from g to kg divide by 1000
1350 ÷ 1000 = 1.35kg
F(x) = 1 - x
f(-3) = 1 - (-3)
f(-3) = 4