Answer:
B-91%
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: arriving home after 7 p.m.
Event B: getting home by bus.
When he chooses to get home by bus, he arrives home after 7 p.m. 25 percent of the time.
This means that 
Because the bus is cheaper, he uses the bus 70 percent of the time.
This means that 
Probability of getting home after 7 p.m.
70% of the time he uses bus, and by bus, he arrives arrives home after 7 p.m. 25 percent of the time.
100 - 70 = 30% of the time he uses the car, and by car, he arrives home after 7 p.m. 6 percent of the time.
So

What is the approximate probability that Matthew chose to get home from work by bus, given that he arrived home after 7 p.m.?

Rouding up, 91%.
So the correct answer is:
B-91%
<span>I = PRT
</span><span>P = 1000
R = 2.5% -- change to a decimal = .025
T = 3
</span>
<span>
now we sub
I = PRT
I = (1000)(.025)(3)
I = 75
</span><span> so at the end of 3 years, there will be : 1000 + 75 = $ 1075 in the account
</span>
Hope this helps!!
~Lena~
<span />
Answer:
71
Step-by-step explanation:
Take the cost of the item and multiply by the commission percent
800 * 8.875%
Change to decimal form
800*.08875
71
By definition of tangent,
tan(<em>x</em>) = sin(<em>x</em>) / cos(<em>x</em>)
so if tan(<em>x</em>) < 0, and we're given cos(<em>x</em>) = -1/4 < 0, then it follows that sin(<em>x</em>) > 0.
Recall the Pythagorean identity:
cos²(<em>x</em>) + sin²(<em>x</em>) = 1 → sin(<em>x</em>) = + √(1 - cos²(<em>x</em>))
Then
sin(<em>x</em>) = √(1 - (-1/4)²) = √(15/16) = √(15)/4
Recall the double angle identity:
sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)
Then
sin(2<em>x</em>) = 2 • √(15)/4 • (-1/4) = -2√(15)/16 = -√(15)/8