Answer:
a) 0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.
b) 0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons
Step-by-step explanation:
We use Venn's Equations for probabilities.
I am going to say that:
P(A) is the probability that a randomly selected person will feel guilty about wasting food.
P(B) is the probability that a randomly selected person will feel guilty about leaving lights on when not in a room.
0.12 probability that a randomly selected person will feel guilty for both of these reasons.
This means that 
0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.
This means that 
0.39 probability that a randomly selected person will feel guilty about wasting food
This means that 
a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.
b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons
Answer:
x = 0
Step-by-step explanation:
There's no horizontal shift.
the answer is 203/16 or 12.6875
Answer: -7 = e
Step-by-step explanation: To solve this equation for <em>e</em>, we need to get <em>e</em> by itself on the right side of the equation. Since <em>e</em> is multiplied by 16, in order to get <em>e</em> by itself, we need to divide by 16 on the right side of the equation. If we divide by 16 on the right side of the equation, we must also divide by 16 on the left side of the equation.
On the right side of the equation the 16's cancel and we have <em>e</em>. On the right side of the equation -112 divided by 16 is -7. Remember that a negative divided by a positive is a negative.
So we have -7 = e which is the solution to our equation.
To check our solution, we can plug -7 in for <em>e</em> in the original equation. So we have -112 = 16 (-7) or -112 = -112 which is a true statement so our answer checks.
There is a trig identity called the sum of 2 angles for sin its<span>
sin(a+b)=sin(a)cos(b)+cos(a)(sin(b)
</span>
You will need to use it. So in your question split the 4x in 2 equal parts 2x and 2x
<span>
</span><span>sin(4x)=sin(2x+2x)
</span>Now using the expansion above you will get
<span>sin(2x+2x)=sin(2x)×cos(2x)+cos(2x)×sin(2x)
</span>And it will simplify to
<span><span>2sin(2x)cos(2x)
I hope this helps you! Good luck :)</span></span>