Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
Using it's concept, it is found that there is a 0.0366 = 3.66% probability that your coach and your friend get orange and you get a fruit-punch.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem, there are 15 bottles.
- 5 are orange, hence the is a 5/15 = 1/3 probability that the coach gets orange, hence P(A) = 1/3.
- After the coach, there will be 14 bottles remaining, of which 4 are orange, hence the probability that the friend gets orange is of P(B) = 4/14 = 2/7.
- For you, there will be 13 bottles remaining, of which 5 will be of fruit-punch, hence the probability you get fruit-punch is of P(C) = 5/13.
The probability of the three outcomes occurring is given by:

0.0366 = 3.66% probability that your coach and your friend get orange and you get a fruit-punch.
More can be learned about probabilities at brainly.com/question/14398287
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Answer:
92.31 km
Step-by-step explanation:
Combined speed = 50+80
= 130 km/hour
Time = 100/130 = 10/13 hours to collide
Speed × time = distance
distance = 10/13 × 120
= 92.30769231 km
Answer:
D.
Step-by-step explanation:
(1/6)*60 = 10
(1/6)*450 = 75
Check your work
75/10 = 7.5
450/60 = 7.5
Correct!
Answer:
D
Step-by-step explanation:
correct answer, thanks for 15 pts